Mary Tyler Moore -- Laura Petrie, The Dick Van Dyke Show; Mary Richards, The Mary Tyler Moore Show.
Betty White -- Rose Nylund, The Golden Girls; Sue Ann Nivens (The Happy Homemaker), The Mary Tyler Moore Show.
Bea Arthur -- Maude Findlay, Maude; Dorothy Zbornak, The Golden Girls.
Raymond Burr -- Perry Mason, Perry Mason; Robert T. Ironside, Ironside.
John Cleese --Basil Fawlty, Fawlty Towers; Various, Monty Python’s Flying Circus.
I added Cloris Leachman and Michael J. Fox because of their TV and movie roles.
Cloris Leachman -- Phyllis Lindstrom, The Mary Tyler Moore Show and Phyllis; Frau Blücher, Young Frankenstein; Ruth Popper (the coach's wife), The Last Picture Show.
Michael J. Fox -- Marty McFly, Back to the Future trilogy; Alex P. Keaton, Family Ties; Mike Flaherty, Spin City.
Added by Chicken Little in a comment:
John Ritter-- Jack Tripper,Three's Company, Reverend Fordwick,The Waltons.
For Betty White (above), I did not include Life with Elizabeth. Life with Elizabeth was produced by a local LA TV station and was a big hit at the time (1953 - 1955), comparable to I Love Lucy. The reruns can only be seen on America One, a low-power TV network (LPTV) and on DVD. I saw the reruns many years ago. Betty White and co-star Del Moore used to more items on the set when no one was looking -- causing lamps, pillows, and ashtrays to jump about when the different takes were assembled into a show. Each episode ended the same way -- pure Betty White: "Elizabeth and Alvin are a married couple who live an ordinary suburban life, but inevitably managed to get into predicaments. At the end of most predicaments, Alvin, in variable degrees of frustration, would say, "I shall leave you now, Elizabeth" and would walk out of sight. The announcer would say, "Elizabeth, aren't you ashamed?" She would slowly nod, but then, with a slightly devilish grin, would vigorously shake her head to indicate she wasn't."
I also forgot to add Harry Morgan to my original list. What a remarkable career he has had! His list of TV and movies at IMDB is mind-bending, including the judge in Inherit the Wind.
- Pete, December Bride and spin-off Pete and Gladys (December Bride was the show that followed I Love Lucy on CBS).
- Officer Bill Gannon, Dragnet.
- Major General Bartford Hamilton Steele, M*A*S*H.*
- Colonel Sherman T. Potter, M*A*S*H.*