I put in as many as I could think of and find information about. I'm sure that I missed a few obvious ones, so feel free to suggest ones if you don't find them. I usually went with the broadcast date of the first episode. For the ones set in other time periods, I went with the best information I could find, or just made my best guess.
April 60,000,000 BC: Dinosaur Earl Sinclair lives in Pangaea with his wife Fran, son Robbie, daughter Charlene, infant Baby and Fran’s mother, Ethyl. Earl works for the Wesayso Corporation.
September 3,4000,000 BC: Fred and Wilma Flintstone live in Bedrock alongside their neighbors, Barney and Betty Rubble.
September 100,000 BC: Astronauts Mac McKenzie and Hector Canfield live in this time period for a while before returning to their own time, bringing a prehistoric family with them.
June 1485: Prince Edmund, the Black Adder, attempts to overthrow his father, King Richard IV.
January 1586: Edmund, Lord Blackadder, serves as a courtier at the court of Queen Elizabeth i.
September 1797: Edmund Blackadder, Esquire, serves as butler to George, the Prince Regent.
April 1865: Captain Wilton Parmenter assumes command of Fort Courage in Kansas.
September 1917: Captain Edmund Blackadder serves on the Western Front in the First World War.
July 1939: Teenager Henry Aldrich lives with his parents, Sam and Alice, and his sister, Mary.
July 1940: Captain George Mainwaring serves in the British Home Guard in Walmington-on-Sea.
September 1942: U.S.A.A.F. Colonel Robert Hogan runs an Allied sabotage and espionage ring out of Stalag 13, a POW camp located near Hammelburg, Germany. Hogan and his men regularly outwit camp commandant Colonel Wilhelm Klink and Sergeant Hans Schultz.
October 1942: Lieutenant-Commander Quinton McHale commands the PT-73 in the South Pacific Theater during World War Two.
December 1942: René Artois runs a café in Nouvion, France, while dealing with both the German occupiers and the French Resistance.
January 1944: California aircraft plant worker Chester A. Riley has various misadventures with his wife, Peg, various other family members, and his friends, neighbors and co-workers.
July 1948: Miss Connie Brooks teaches English at Madison High School. Her boss is Principal Osgood Conklin.
October 1950: Entertainers George Burns and Gracie Allen have various misadventures.
October 1951: Housewife Lucy Ricardo shares an apartment in New York City with her husband, bandleader Ricky. They frequently socialize with their landlords, Fred and Ethel Mertz.
June 1952: Margie Albright lives in New York City with her father, Vern.
July 1952: Robinson J. Peepers teaches junior high school science in Jefferson City.
October 1952: Entertainers Ozzie and Harriet Nelson live with their sons, David and Ricky.
September 1953: Entertainer Danny Williams lives in New York City with his wife, Margaret and their children, Terry and Rusty.
January 1954: Howard and Marion Cunningham live in Milwaukee, Wisconsin, with their children, Chuck, Richie and Joanie.
October 1954: Jim and Margaret Anderson live with their children, “Princess”, “Bud” and Kitten”.
September 1955: Sergeant Ernie Bilko serves at the U.S. Army base Fort Baxter in Rosevale, Kansas.
October 1955: Brooklyn bus driver Ralph Kramden lives with his wife, Alice. They frequently socialize with their neighbors, Ed and Trixie Norton.
September 1957: Beverly Hills, California attorney Bentley Gregg raises his nice, Kelly, after the accidental death of her parents.
October 1957: Ward and June Cleaver live with their sons, Wally and Theodore. The latter is known as “The Beaver”.
January 1958: Brewery workers Laverne DeFazio and Shirley Feeney share an apartment in Milwaukee, Wisconsin.
January 1958: Housewife Donna Stone and her pediatrician husband, Alex, live with their children, Mary and Jeff.
September 1960: Widower Steven Douglas lives with his sons, Mike, Rob and Chip, and his father-in-law, “Bub” O’Casey.
October 1960: Andy Taylor serves as sheriff of Mayberry, North Carolina. His deputy is Barney Fife. Andy lives with his son, Opie, and his Aunt Bea.
September 1961:
- N.Y.P.D. officers Gunther Toody and Francis Muldoon drive Car 54 of the 53rd Precinct.
- Maid Hazel Burke works for George and Dorothy Baxter.
- Architect Wilbur Post discovers that his horse, Mister Ed, can talk.
October 1961: Television comedy writer Rob Petrie lives in New Rochelle, New York, with his wife, Laura, and their son, Ritchie.
June 1962: London rag-and-bone man Albert Steptoe has a contentious relationship with his son, Harold.
September 1962: After striking oil on his land near Silver Dollar City, Missouri, Jed Clampett moves to Beverly Hills, California with his daughter, Elly May, his mother-in-law, “Granny” Daisy Moses and Jed’s first cousin once removed, Jethro Bodine. They have frequent dealings with their banker, Milburn Drysdale and his secretary, Jane Hathaway.
October 1962: Widow Lucy Carmichael lives in Danfield, New York, with children, Chris and Jerry, and her friend, Viv Bagley and her son, Sherman.
September 1963:
- Journalist Tim O’Hara takes in a shipwrecked Martian that he presents as his “Uncle Martin”.
- Cathy Lane comes to live with her identical cousins, Patty, and Patty’s parents, Martin and Natalie, and Patty’s brother, Ross.
- Kate Bradley runs the Shady Rest Hotel - which is midway between Hooterville and Pixley – along with her daughters, Billie Jo, Bobbie Jo and Betty Jo, and her uncle, Joe Carson.
September 1964:
- Gomez Addams shares a house on Cemetery Lane with his wife, Morticia, their son, Pugsley, their daughter, Wednesday, Gomez’s mother, known as “Grandmama”, Morticia’s uncle, Fester Frump, their butler, Lurch and Thing, a disembodied hand.
- A witch named Samantha marries mortal advertising executive Darrin Stephens, much to the chagrin of her mother, Endora.
- Caught in a sudden storm, the S.S. Minnow is shipwrecked on a desert island. The passengers and crew survive on the island for many years. The castaways include Skipper Jonas Grumby, his first mate, Gilligan, Thurston Howell III and his wife, Lovey, movie star Ginger Grant, Professor Roy Hinkley and Mary-Ann Summers.
- Gomer Pyle joins the United States Marine Corps.
- Mortuary worker Herman Munster lives in Mockingbird Heights, California with his wife, Lily, their son Eddie, their niece Marilyn and Lily’s father, “Grandpa” Sam Dracula.
September 1965:
- Maxwell Smart is Agent 86 of CONTROL, serving under the Chief alongside Agent 99. They battle the agents of KAOS, in particular, Max’s nemesis, Siegfried.
- Gidget Lawrence lives with her father, Russ, in southern California.
- Manhattan attorney Oliver Douglas moves to a farm in Hooterville with his wife, Lisa.
- Astronaut Tony Nelson discovers a genie called “Jeannie” on a deserted island. She comes to live with him in his home in Cocoa Beach, Florida.
- Attorney David Crabtree’s deceased mother is “reincarnated” as an antique automobile.
September 1966:
- Engineer Bill Davis shares his home in New York City with his nieces Cissy and Buffy, his nephew, Jody and his butler, Mister French.
- Astronauts Mac McKenzie and Hector Canfield travel back to prehistoric times while on a space mission. They eventually return to their own time, bringing a prehistoric family with them.
- Musicians Davy Jones, Mickey Dolenz, Mike Nesmith and Peter Tork form and rock and roll band called “The Monkees”.
January 1967: Police chemist Carter Nash becomes the super-hero Captain Nice.
September 1967: A nun called Sister Bertrille lives at the Convent San Tanco in Puerto Rico.
September 1968: Widow Lucy Carter lives in Los Angels, California, with her children, Kim and Craig. She works for her brother-in-law Harry at Carter’s Unique Employment Agency.
September 1969:
- Mike and Carol Brady marry and combine their families, sharing their home with Mike’s sons Greg, Peter and Bobby and Carol’s daughters Marcia, Jan and Cindy, as well as their maid, Alice.
- Widower Tom Corbett lives in Los Angeles, California, with his son, Eddie. Their housekeeper is Mrs. Livingston.
- Widow Carolyn Muir and her children move into Gull Cottage in Schooner Bay, Maine, only to find that it is haunted by the ghost of its former owner, Captain Edward Gregg.
January 1970: Nanny Phoebe Figalilly goes to work for Professor Harold Everett.
September 1970:
- Blue collar worker Arnie Nuvo is promoted to an executive position at the Continental Flange Conpany.
- Mary Richards works as an associate producer at WJM-TV in Minneapolis, Minnesota. Her colleagues include producer Lou Grant, head writer Murray Slaughter and anchorman Ted Baxter. She often socializes with her friend Rhoda Morgenstern and landlady Phyllis Lindstrom.
- Shirley, Keith, Laurie, Danny, Chris and Tracy Partridge form a band together. Their manager is Reuben Kincaid.
- Two divorced men – Felix Unger and Oscar Madison – share an apartment in New York city.
January 1971: Archie Bunker lives in Queens, New York with his wife, Edith, their daughter, Gloria, and her husband, Michael Stivic.
January 1972: Junk dealer Fred G. Sanford lives in the Watts neighborhood of Los Angeles. He has a contentious relationship with his son, Lamont.
September 1972:
- Mister Rumbold serves as the floor manager for the men’s and women’s clothing departments of Grace Brothers department store, whose staff includes Mister Humphries, Mrs. Slocombe, Miss Brahms, Captain Peacock, Mister Grainger and Mister Lucas, among others.
- Psychologist Bob Hartley lives in Chicago with his wife, Emily.
- Irish Catholic teacher Bridget Fitzgerald marries Jewish cab driver Bernie Steinberg.
- Maude Findlay lives in Tuckahoe, New York, with her husband, Walter, her daughter, Carol Trayner, and Carol’s son, Philip.
February 1974: Florida and James Evans live in Chicago with their children, J.J., Thelma and Michael.
September 1974: Chico Rodriguez goes to work at Ed Brown’s garage in East Los Angeles, California.
October 1974: “C.D.” Danbee and Clara Burrell fall in love and eventually get married.
January 1975:
- Police Captain Barney Miller leads the Twelfth Precinct of the N.Y.P.D., commanding Detectives Wojciehowicz, Harris, Fish, Yemana, Amenguale, Dietrich and others.
- Dry-Cleaner George Jefferson, his wife Louise, and their son Lionel, move into a high-rise on Manhattan’s Upper East Side.
September 1975:
- Basil Fawlty and his wife Sybil run Fawlty Towers, a hotel in Torquay in Devon in the U.K.
- Gabe Kotter returns to teach at his alma mater, James Buchanan High School in Brooklyn, New York. His students include Vinnie Barbarino, Freddie “Boom-Boom” Washington, Juan Epstein and Arnold Horshack.
December 1975: Divorcee Ann Romano moves to Indianapolis with her daughters, Julie and Barbara Cooper.
August 1976:
- After her husband is killed, Alice Hyatt settles in Phoenix, Arizona, with her son, Philip. She takes a job as a waitress at Mel Sharples’ diner, alongside her co-workers Flo Castleberry and Vera Gorman.
- Six teenagers living in Point Place, Wisconsin – Eric Forman, Jackie Burkhart, Michael Kelso, Steven Hyde, Donna Pinciotti and Fez – have various misadventures together.
- “Raj” Thomas lives in the Watts section of Los Aneles, California, with his mother, Mabel, and his younger sister, Dee. He frequently socializes with his friends, “Rerun” Stubbs and Dwayne Nelson, at Rob’s Place, a soda shop staffed by waitress Shirley Nelson.
September 1976: Columnist Richard Barrington romances photographer Charley Drake.
December 1976: C.P.O. Otto Sharkey us in charge of Company 144, a group of U.S. Navy recruits in San Diego, California.
March 1977: Jack Tripper shares an apartment in Santa Monica, California with Janet Wood and Chrissy Snow.
September 1977: Rob Mobey serves as the police chief of Clinton Corners, Georgia.
September 1978:
- Mork from Ork lands on Earth in Boulder, Colorado, where he is befriended by Mindy McConnell.
- Alex Rieger works for the Sunshine Cab Company in New York City alongside fellow cabbies Bobby Wheeler, Elaine Nardo, Tony Banta and Jim Ignatowski, as well as dispatcher Louie DePalma and mechanic Latka Gravas.
- Andy Travis becomes the program director for radio station WKRP in Cincinnati, Ohio, alongside general manager Arthur Carlson, DJ’s Doctor Johnny Fever and Venus Flytrap, newsreader Les Nessman, sales manager Herb Tarlek, and Bailey Quarters, who handles billing and station traffic.
November 1978: Businessman Philip Drummond adopts brothers Arnold and Willis Jackson, who come to live with him and his daughter, Kimberly.
January 1979: Radio talk show host Larry Alder lives in Portland, Oregon, with his daughters, Diane and Ruthie.
February 1979: Waitress Angie Falco lives in Philadelphia, Pennsylvania, with her mother, Theresa, and younger sister, Marie. She romances and eventually marries Bradley Benson, a pediatrician.
August 1979: Edna Garrett becomes a housemother at the Eastland School in Peekskill, New York. The students she oversees include Blair Warner, Tootie Ramsey, Natalie Green and Jo Polniaczek.
September 1979: Benson DuBois serves as head of household to Governor Eugene Gatling.
November 1980:
- Struggling ad men Kip Wilson and Henry Desmond pose as women in order to live in the women-only Susan B. Anthony Hotel.
- Cartoonist Henry Rush lives in San Francisco, California, with his wife, Muriel, and adult daughters Jackie and Sara.
October 1981: In Glenlawn, California, Nell Harper looks after police chief Carl Kanisky and his daughters, Katie, Julie and Samantha.
September 1982:
- Former baseball player Sam Malone operates the bar “Cheers” in Boston, Massachusetts.
- Steven and Elyse Keaston live in Columbus, Ohio, with their children, Alex, Mallory and Jennifer.
- In Oakland, California, gym coach Mark Cooper lives with his roommate, Vanessa Russell.
- Ricky Stratton comes to live with his father, Edward Stratton III.
October 1982: Dick and Jessica Loudon operate the Stratford Inn in Vermont.
November 1982: Four university students – Mike, Neil, Vyvyan and Rick – share a London flat that they rent from Jerzei Balowski.
January 1983: Widowed “Mama” Thelma Harper lives in Raytown with her family and friends.
January 1984: Judge Harry Stone oversees the night shift of a Manhattan criminal court.
March 1984: Friends Kate McArdle and Allie Lowell share a home in Greenwich Village in New York City.
September 1984:
- Obstetrician Cliff Huxtable and his wife, Clair, a lawyer, live in Brooklyn Heights, New York, with their children, Sondra, Denise, Theo, Vanessa and Rudy.
- Building manager George Warnimont takes in abandoned child “Punky” Brewster.
- Former baseball player Tony Miceli moves to Fairfield, Connecticut, with his daughter, Samantha. He takes a job as a live-in housekeeper for Angela Bower, He frequently interacts with Angela’s son, Jonathan, and her mother, Mona Robinson.
October 1984: A college student named Charles takes a job as a live-in housekeeper for Stan and Jill Pembroke in New Brunswick, New Jersey. He has various misadventures with his best friend, Buddy Lembeck.
March 1985: Butler Lynn Belvedere works for George and Marsha Owens, who live in Pittsburgh, Pennsylvania, with their children, Kevin, Heather, and Wesley.
September 1985:
- Blanche Devereaux, Rose Nylund, Dorothy Zbornak and Dorothy’s mother, Sophia Petrillo share a home in Miami, Florida.
- Doctor Jason Seaver lives in Huntington, Long Island, with his wife, Maggie, and their children, Mike, Carol and Ben.
- Inventor tTed Lawson brings a robot little girl named V.I.C.I. (also called “Vicki”) to live with his wife, Joan, and son, Jamie.
- Mary Jenkins lives at 227 Lexington Place in Washington, DC, with her husband Lester, her daughter Brenda and neighbor, Sandra Clark.
March 1986: Balki Bartokomous comes to live with his distant cousin, Larry Appleton, in Chicago, Illinois.
September 1986:
- Melmacian Gordon Shumway crash-lands on Earth and takes up residence with the Tanner family.
- Lawyer Ernest Frye serves as a deacon at the First Community Church of Philadelphia, Pennsylvania.
- Julia Sugarbaker, Suzanne Sugarbaker, Mary Jo Shively and Charlene Frazier work at the Atlanta, Georgia, design firm, Sugarbaker & Sugarbaker.
- Charlie Moore teaches history at Millard Fillmore Hogh School in Manhattan.
April 1987: Chicago shoe salesman Al Bundy lives with his wife Peg, daughter Kelly and son Bud.
September 1987:
- Denise Huxtable attends Hillman College in Virginia.
- Danny Tanner lives in San Francisco, California, with his three daughters, D.J., Stephanie and Michelle, as well as his friends, Jesse Katsopolis and Joey Gladstone.
- On her thirteenth birthday, Evie Garland discovers that her father, Troy, is an alien. She lives in Marlowe, California, with her mother, Donna.
- Hildy Granger becomes the Sherriff of Lakes County, Nevada, after the death of her husband.
October 1988:
- After his wife dies, Miami, Florida, pediatrician Harry Weston’s adult daughters, Carol and Barbara, move in with him.
- Roseanne and Dan Conner live in Lanford, Illinois, with their daughters Becky and Darlene, and their son, D.J.
February 1989: Hayden Fox serves as the coach of the Minnesota State University Screaming Eagles football team.
July 1989: Stand-up comedian Jerry Seinfeld has various misadventures in New York City alongside his friends George Costanza, Elaine Benes and Cosmo Kramer.
September 1989:
- Teenager Doogie Howser is resident surgeon at Eastman Medical Center in Los Angeles, California.
- Policeman Carl Winslow lives in Chicago, Illinois, with his wife, Harriette and their children, Eddie, Laura Lee and Judy.
- Major John D. MacGillis serves at Camp Singleton. He meets and eventually marries journalist Polly Cooper, who has three daughters, Elizabeth, Rovin and Casey.
December 1989: Nuclear power plant worker Homer Simpson lives in Springfield with his wife, Marge, their son, Bart, and their daughters, Lisa and Maggie.
September 1990: After an incident with gang members, West Philadelphia teenager Will Smith is sent to live with his aunt and uncle in Bel Air, California.
January 1991: Teenager Blossom Russo lives with her father, Nick, and her brothers, Tony and joey.
September 1991:
- Manhattan research assistant Herman Brooks has voices in his mind directing his thoughts and actions.
- Tim and Jill Taylor live in suburban Detroit with their sons, Brad, Randy and Mark. Tim hosts Tool Time, a home improvement show.
September 1992:
- Cartoonist Bob McKay works for Ace Comics.
- Newlyweds Paul and Jame Buchman have various misadventures living in Greenwich Village in New York City.
November 1992: Public relations mogul Edina Monsoon lives with her daughter, Saffron, and frequently socializes with her friend, magazine fashion director, Patsy Stone.
September 1993:
- Psychiatrist Frasier Crane returns to Seattle, Washington, to host a radio talk show. Once there, he reconnects with his father, Martin, and his younger brother, Niles.
- Grace Kelly lives in Victory, Missouri, with her children Quentin, Libby and Patrick
November 1993: In New York City, Broadway producer Maxwell Sheffield hires Fran Fine to be a nanny for his three children, Maggie, Brighton and Gracie
January 1994: New York film critic Jay Sherman hosts a TV show called Coming Attractions.
March 1994: Ellen Morgan works at a bookstore in Los Angeles, California.
September 1994: Friends Rachel Green, Monica Geller, Phoebe Buffay, Joey Tribbiani, Chandler Bing and Ross Geller have various misadventures living in New York City.
November 1994: Geraldine Granger becomes the vicar of Dibley in Oxfordshire in the United Kingdom.
April 1995: Priests Ted Crilly, Dougal McGuire and Jack Hackett live together on Craggy Island.
May 1995: Doctor Jonathan Katz works as a professional psychotherapist.
September 1995:
- Manhattan cartoonist Caroline Duffy has various misadventures with her friends and neighbors.
- Drew Carey works for the Winfred-Louder department store in Cleveland, Ohip.
September 1996:
- Sportswriter Ray Barone lives on Long Island with his wife, Debra, and their children, Allie, Matthew and Geoffrey. Ray’s parents, Marie and Frank, live across the street with their older son, Robert.
- Sabrina Spellman lives in Westbridge, Massachusetts, with her Aunts Hilda and Zelda, and their cat, Salem. On her sixteenth birthday, she discovers that she is a witch.
January 1997: Propane salesman Hank Hill lives in Arlen, Texas, along with his wife, Peggy, their son, Bobby, and Hank’s niece, Luanne.
March 1997: Daria Morgendorffer lives in Lawndale with her parents, Jake and Helen, and her younger sister, Quinn Daria frequently socializes with her friend, Jane Lane.
August 1997: Grade-schoolers Stan Marsh, Kyle Broflovski, Eric Cartman and Kenny McCormick have various misadventures in and around their hometown of South Park, Colorado.
September 1997: San Francisco yoga instructor Dharma Finklestein and lawyer Greg Montgomery elope on their first date.
September 1998: Doug and Carrie Heffernan live in Rego Park, Queens, New York.
January 1999:
- Engineer Dilbert has various misadventures with his colleagues Wally and Alice, and his dog, Dogbert.
- Peter and Lois Griffin live in Quahog, Rhode Island, with their children Meg, Chris and Stewie, and their dog, Brian.
December 1999: New York City pizza delivery man Philip J. Fry is accidentally frozen in suspended animation.
January 2000: Malcolm Nolastname lives with his parents, Hal and Lois, and his brothers, Francis, Reese and Dewey.
July 2001: David Brent serves as the general manager of the Slough branch of the Wernham Hogg paper company in the United Kingdom.
May 2005: Michael Scott serves as the regional manager of the Scranton, Pennsylvania branch of the Dunder Mifflin paper company.
November 2005: Robert Riley moves to Woodcrest with his grandsons, Huey and riley.
March 2006: Teenager Miley Stewart is secretly pop singer Hannah Montana.
October 2006: Liz Lemon serves as head writer and showrunner for the NBC sketch comedy series TGS with Tracy Jordan.
September 2007: Pasadena, California physicists Leonard Hofstadter and Sheldon Cooper have various misadventures with their friends and neighbors.
April 2009: Leslie Knope works as a bureaucrat in the Parks and Recreation Department in Pawnee, Indiana.
September 2009:
- Cleveland Brown lives in Stoolbend, Virginia, with his new wife, Donna, and their children, Cleveland Jr., Roberta and Rallo.
- Businessman Jay Pritchett lives in suburban Los Angeles with his wife, Gloria, and their several children and grandchildren.
September 2010: Melanie Moretti, Joy Scroggs and Victoria Chase share a home in Cleveland, Ohio, with caretaker Elka Ostrovsky.
January 2011: Bob Belcher, his wife, Linda, and their children, Tina, Gene and Louise, run the restaurant Bob’s Burgers in Seymour’s Bay, New Jersey.
October 2014: CIA agent Stan Smith lives in Langley, Virginia, with his wife, Francine, daughter, Hayley, and son, Steve.
September 2062: George and Jane Jetson live in Orbit City with their daughter Judy, son Elroy, dog Astro and robot maid, Rosie.
February 2226: Adam Quark serves as the captain of a United Galaxy Sanitation Patrol Cruiser.
December 2999: Philip J. Fry is revived in New New York City. He goes to work for Planet Express delivery company alongside mutant Turanga Leela and robot Bender Rodriguez.
Replies
Everybody Loves Raymond begins 1996.
Ah, good one! Added.
Added Perfect Strangers and Modern Family.
Bob Newhart's third sitcom titled Bob ran in 1992/93. The first season he portrayed a comic book artist with one episode featuring Jack Kirby and several other comic book pros. The second, short lived season Bob switched to being a greeting card artist.
Added Bob.