I was also going to say Belzer/Munch, but it’s weird little connections you like, I suggest exploring the tommyverse.
Alan Rosenberg and Debi Mazar of Civil Wars played the same roles as lawyer Eli Levinson and secretary Denise Iannello on L.A. Law after *Civil Wars * was cancelled.
I’ve always found the “Tommy Westphall Universe” stuff to be pretty fascinating.
As far as television show crossovers go, the greatest has to be the Magnum P.I./Simon & Simon crossover episodes. (At least it was when I was 14). 
Kramer once appeared on Mad About You. Paul goes back to his old apartment, to get some of his stuff that he left there with his buddy who took over the lease, and discovers that Kramer has taken over the lease from his buddy.
Bob Newhart played Bob Hartley on The Bob Newhart Show, in the final episode of Newhart, and in an episode of Murphy Brown. Jack Riley played Hartley’s patient Elliot Carlin on The Bob Newhart Show, Newhart, and St. Elsewhere.
One of the weirdest crossover appearances ever done was by Enos Straight (Sonny Shroyer) and Boss Hogg (Sorrell Booke) appeared on an episode of Alice. Boss had some scheme to take over Mel’s Diner. (Why a millionaire businessman from small town Georgia would have the most remote desire for a two bit greasy spoon in Phoenix, Arizona I have no idea, but I’m sure it was explained on the episode.) Shroyer also had a Dukes spinoff, thus he played Enos on at least three series.
Roseanne had several “fantasy episode” guest stars: one featured Jennifer Saunders and Joanne Lumley played Edina and Patsy from Absolutely Fabulous, another featured Ed Asner as Lou Grant, and perhaps the most famous was all of the then-surviving cast members of Gilligan’s Island- Bob Denver, Dawn Wells, Tina Louise, and Russell Johnson, though they didn’t reprise their G.I. roles but played the cast members of Roseanne who had played their roles in a dream sequence (hard to explain if you didn’t see it, but here’s the clip- I don’t think anybody in the studio audience recognized Tina Louise).
Carol Burnett and Vicky Lawrence appeared as Eunice Higgins and Thelma “Mama” Harper on The Carol Burnett Show, Mama’s Family, in a 1982 comedy-drama movie of the week, and the gameshow Password (on which they appeared in character).
Not quite what the OP asked for, but… one 1987 episode of Murder She Wrote was a sequel to a 1949 B movie, Strange Bargain, and featured Harry Morgan and several other actors as their characters from that movie.
Coming back around, though, Jessica Fletcher and Thomas Magnum took turns guesting on each other’s shows.
(Selleck also showed up in THE FALL GUY, but only as “Tom Selleck, the guy who’s about to film a scene for MAGNUM PI”; I mention this because Lou Ferrigno went a step further in that same two-parter, as we see the Hulk crash through a wall to beat the hell out of a gun-toting Lee Majors for a while before the director yells cut and we see it’s just our favorite stuntman earning a paycheck on the set as usual; Ferrigno then casually walks over to talk with his agent about that role he’s up for as a deaf cowboy…)
A couple characters flipped from Buffy to Angel after the latter series started: Wesley Wyndham-Pryce (Alexis Denisof) and Spike (James Marsters); Wesley swapped shows in the middle of Angel’s first season and didn’t appear on Buffy after Angel had been spun off, so maybe would still be considered a spinoff character, but Spike had several seasons in Buffy before swapping to Angel for that show’s final season.
I also remember an episode of a series called Day by Day that featured much of The Brady Bunch cast. And per Wikipedia, Robert Reed and Florence Henderson appeared as their characters in a couple of other shows, including The Love Boat, along with a long list of Brady-related shows.
How soon they forget: Jenna Elfman and Thomas Gibson as Dharma & Greg on the season opener of 2 and a Half Men.
John Houseman, who won an Oscar playing snooty law professor Charles Kingsfield in the movie The Paper Chase later played Kingsfield in…
-
The TV series The Paper Chase
-
An episode of the short-lived sitcom The Associates (starring the young Martin Short)
-
An episode of the sitcom 227, in which he’d been hired by Jackee Harry to sue her friends for a share of royalties to a song they’d written.
I remember an episode of St. Elsewhere on which several of the doctors stopped to get a few drinks at a local Boston bar… which turned out to be Cheers. Rhea Perlman waited on them, and George Wendt was one of the doctor’s accountant.
As William Daniels left the bar, he pointed at Rhea and said, “Stiff her- but good.”
As I recall, the crossover fell flat. It seemed like an inspired idea, but it just didn’t work at all.
I think the ER doctors were on Friends, too, weren’t they — Greene and George Clooney?
George Clooney and Noah Wyle played ER doctors on Friends, but I don’t think they played their characters from ER. Probably b/c the writers couldn’t come up with why two ER doctors from Chicago were working in Manhattan.
George Clooney and Noah Wyle did play two ER doctors on an early Friends episode. They were not, however, Doctors Ross and Carter.
I see I got ninja’d on that, but here’s the episode cast list.
In a similar vein, when the Banks family sold their mansion on Fresh Prince of Bel Air two of the interested buyers were Philip and Arnold Drummond from Diff’rent Strokes. The house sold to George and Louise Jefferson (still with Florence in tow) from The Jeffersons, which was actually the second FPoBA episode to feature Hemsley and Sanford as The Jeffersons. (They were seen in a marriage counselor’s office in the previous one; Louise was furious at George by calling her Wheezy now that she had asthma.)
So, shows the Jeffersons appeared on:
All in the Family
The Jeffersons
Checking In (a very brief spin-off revolving around Florence)
Fresh Prince of Bel Air
Hemsley and Sanford were also in a series of commercials for, I think, Denny’s (or Ihop?) and for Old Navy, but were never identified as the Jeffersons (though it was an assumption).
Gary Coleman appeared as Arnold Jackson-Drummond on Diff’rent Strokes, Facts of Life, Silver Spoons (a double crossover- Ricky Schroder appeared on Diff.Str. in a two part caper episode), and Fresh Prince.
A funny non-reprisal of characters was when Jean Stapleton and Carroll O’Connor appeared on Donny & Marie, their first talk show together in the 20+ years since Stapleton left the show (and O’Connor’s last talk show appearance). D&M ask them if they can please do their character voices one more time and Stapleton says, politely but firmly, “No”. She had no interest in it.
Also Cordelia, and, obviously, Angel, plus several other main Buffy characters in guest roles. But it’s not surprising for a spin-off to include some of the main characters of the parent show. While TNG and DS9 are set in the same fictional universe, they’re not spin-offs of each other.
Don’t really see the distinction there; I’d definitely call DS9 a TNG spin-off.
Do you consider all the Star Trek shows to be spin-offs of the original series? To me it seems like there’s too little crossover, in terms of plot and characters, for them to be spin-offs. Worf and O’Brien were the only characters to cross over as regulars; I’m not sure if there were even any guest appearances from other characters, but I’m sure someone else here knows.
Spin-offs are usually taking one character (or occasionally a family) from a show and basing a whole new series around them. The NCIS and CSI spin-offs don’t do that, but they’re exactly the same as the parent shows in plot types and atmosphere as well as being the same organisation. (Law and Order perhaps too, but I haven’t seen any of that).
Picard’s in the first episode!
…and I think this should get an asterisk in its own rite as one was a comedy and one was a drama.