The recent death of Rue McClanahan reminds me that she played opposite two different actors on three different TV shows:
Rue McClanahan & Bea Arthur–Maude & The Golden Girls
Rue McClanahan & Betty White–Mama’s Family & The Golden Girls
The other three sets of actors I could think of:
Fran Drescher & Charles Shaughnessy: The Nanny & Life with Fran
Bill Cosby & Phylicia Rashād : The Cosby Show & Cos
Johnny Galecki & Sara Gilbert: Roseanne & The Big Bang Theory
Note: Gyest stars do not count. The actor must play at least a recurring role.
Lucille Ball and Gale Gordon – The Lucy Show and Here’s Lucy
Lucille Ball and Vivian Vance – I Love Lucy and The Lucy Show
Peter Lind Hayes and Mary Healy – The Peter Lind Hayes Show and Peter Loves Mary (It helped that they were married)
Tim Conway and Joe Flynn – McHale’s Navy, The Tim Conway Show
Gale Gordon was a regular on Lucille Ball’s The Lucy Show and Here’s Lucy (he was essentially playing the same character with a different name). According to IMDb, he was a regular, guest star, or co-star on five series with Lucille Ball (if you count the Lucy-Desi Comedy Hour as a separate series).
OK, Tom Poston had a recurring role (5 episodes) as Bob’s college buddy on The Bob Newhart Show before being cast as a regular (the dimwitted handyman) on Newhart.
Oh, I’ve remembered more - the whole Sorkin cast of regulars:
Evan Handler, Matthew Perry and Bradley Whitford: “The West Wing” and “Studio 60 on the Sunset Strip”
Mary McCormack, Josh Malina, Allison Janney: “The West Wing” and “In Plain Sight”
Josh Malina and Teri Polo: “Sports Night” and “The West Wing” (I would include Lisa Edelstein, but her character was gone by the time Malina joined the cast, so they never played opposite each other.)