And the people have to be a regular, not an occasional guest star.

To get it started--

Lucille Ball and Vivian Vance-- I Love Lucy, The Lucy Show
Lucille Ball and Gale Gordon--The Lucy Show, Here's Lucy
Bill Cosby and Phylicia Rashad--The Cosby Show, Cosby
Michael Landon and Victor French-- Little House, Highway to Heaven

ok--now go :)

Bea Arthur and Rue McClannahan-"MAUDE", "THE GOLDEN GIRLS"

scott baio and lynda goodfriend happy days and who;s watching the kids

Betty White/Rue Mclanahan - Golden Girls/Mamas Family

Al Lewis and Fredd Gwynne: Car 54, Where are You? and The Munsters
Dick Gautier and Bernie Kopell: Get Smart and When Things were Rotten
Richard Mulligan and Dinah Manoff: Soap and Empty Nest

Clifton Davis and Jester Hairston: That's My Mama and Amen

Alan Ruck and Heather Locklear - Going Places and Spin City
Sid Caesar, Howard Morris and Carl Reiner - Your Show of Shows and
Caesar's Hour
Jackie Gleason and Art Carney - Cavalcade of Stars and The Honeymooners
Andy Griffith and Don Knotts - Andy Griffith Show and Matlock
(Knotts was a semi-regular in a recurring role as neighbor Les Calhoun)
Danny Thomas, Marjorie Lord, Rusty Hamer, Angela Cartwright, Sid Melton,
and Hans Conreid - The Danny Thomas Show and Make Room for
Granddaddy

I don't think your last one counts, as MAKE ROOM FOR DADDY and THE DANNY THOMAS SHOW were the same series, they just changed the name.

The Matlock one probably wouldn't count either, as Don Knotts wasn't a regular, just an occasional guest appearance (if all his apperances are listed on the tv.com guide, he only appeared 12 times throughout the series)
I do have one though, Telma Hopkins and Rosetta LeNoire were on both Gimme a Break! and Family Matters. Rosetta was only recurring at first on GAB, but on the last season, she was a credited star, so this should count :)

Joey Lawrence and Matthew Lawrence - Gimme a Break! and Brotherly Love
Larry Hagman and Barbara Eden - I Dream of Jeannie and Dallas. Barbara Eden was a guest star originally, but got a spot in the opening credits in one of "Dallas" final seasons.

sara gilbert and johnny galecki- roseanne and the big bang theory

sara gilbert and johnny galecki- roseanne and the big bang theory

Is Sara a regular on this show? (I don't watch it).

Is Sara a regular on this show? (I don't watch it).

actually, i just checked on imdb and sadly she isn't, although johnny is