Same character played by the same actor on different shows.

Kelsey Grammer played “Frasier Crane” on three unrelated shows and one TV film: Cheers (and the eponymous spin-off), The John Larroquette Show, Wings, and The Earth Day Special (1990): http://www.imdb.com/character/ch0014243/.

Lots of crossover on the Happy Days universe shows:

Henry Winkler played Fonzie on Happy Days, Laverne and Shirley, and Joanie Loves Chachi.
Scott Baio played Chachi and Erin Moran played Joanie on *Happy Days *and Joanie Loves Chachi
Penny Marshall and Cindy Williams played Laverne and Shirley on *Happy Days *and Laverne and Shirley
Robin Williams played Mork from Ork on *Happy Days *and Mork and Mindy

Also, Carroll O’Connor played Archie Bunker on *All in the Family *and Archie Bunker’s Place,
Gary Coleman played Arnold on *Diff’rent Strokes *and The Facts of Life, and
Charlotte Rae played Edna Garrett on *Diff’rent Strokes *and *The Facts of Life
*

Don Davis played Gen Hammond in Stargate SG-1, Stargate Atlantis, Stargate Continuum, and Stargate Children of the Gods.

He’d probably be in the newest series too if it weren’t for dying at only age 65.

There were several other Stargate Actors that appeared in all the Gate series too.

It appears that John Ratzenberger and George Wendt, played Norm and Cliff on a number of programs as well.

Cheers
Fraiser (Cheers spin-off)
The Tortellis (Cheers spin-off)
Wings
St. Elsewhere
The Simpsons (if you count voice work)

A few more voice actors who have reprised roles from other shows on the Simpsons;

-David Duchovny and Gillian Anderson as Agents Mulder and Scully.
-Patrick McGoohan as Number Six.
-Jon Lovitz as Jay Sherman (The Critic).
-George Takei as Mr. Sulu.
-Kiefer Sutherland and Mary Lynn Rajskub as Jack Bauer and Chloe O’Brian.
-Mike Judge as Hank Hill.

Kudrow had appeared as Ursula on *Mad About You several times before being cast on Friends, and the roles were not initially meant to have any connection. The story I recall hearing is that when the Friends writers decided to introduce Phoebe’s twin sister (about 2/3 into the first season), somebody in the room had a light-bulb moment and said “what if Phoebe’s sister is Ursula the waitress?” and everyone loved the idea.
*from DVD commentary, I think, for what it’s worth

They played it coy on I Love Lucy by having everyone refer to George Reeves as “Superman”: it’s never made 100% clear whether (a) he’s just an actor wearing the costume for an in-character appearance or whether (b) the Last Son Of Krypton is casually shoving a piano aside to save that poor woman out on the balcony.

(Puts Trekker geek hat on.)
Not quite. Armin played other Ferengi on TNG before DS9, but the only time he ever appeared as Quark on TNG is in the episode ‘Firstborn’, which is after DS9 premiered.
(Takes hat back off.)

If you want to stretch a point, Cliff Arquette played Charley Weaver in about a dozen different TV shows.

Michael Dorn’s situation was unique. He played Worf on TNG and later on DS9 as regular recurring roles. But he wasn’t spin off into his own starring sequel series.

I can’t think of another situation like this except General Hammond in the various Stargate shows and his role was never as prominent as Worfs. Most of the posts here refer to rare guest appearances on other shows. Or sequel spinoffs of a character.

He wasn’t actually Colonel Klink on The Simpsons. he was just assuming his form.

Does his appearance on 30 ROCK count?

Ted Cassidy appeared on Batman as his character Lurch from the Addams Family.

Bruce Lee appeared as Kato, with Van Williams as his sidekick the Green Hornet.

I’m wondering if his appearance on Sesame Street counts.

(Actually, I found out that’s not really Richard Belzer…for some reason I thought he played the Munch puppet, or at least provided the voice for it.)

There’s also the other Cheers characters, like Woody and Diane, who make appearances in Frasier.

Well, not entirely unique, since the aforementioned Miles O’Brien was in both shows too. He wasn’t as important a character in TNG as in DS9, but he was in multiple episodes. I agree, though - it is unusual.

The aforementioned Oscar Goldman was second-billed on both shows.

He also appeared as a Munch-like cop on Mad About You, but it wasn’t technically Munch.

IIRC, Emma Samms began on Dynasty as Fallon in #5, and then moved to The Colbys for that series’ short run, before merging back into Dynasty and continuing to the end in 1989.

How many things has Father Guido Sarduchi made appearances in? He’s gotta be up there with Belzer’s character for sheer number.