Some people in this thread already started using the wording that helps find these sorts of things. Crossovers are what they’re typically called, and when you Google variations of the term for TV you should get a bunch of lists including Wikipedia pages. http://en.wikipedia.org/wiki/List_of_fictional_crossovers
If you specifically mean instances where episodes from two or more series continue the story rather than just characters crossing over, that narrows the list somewhat.
The Law and Order franchise plus Homicide: Life on the Street were the ones I immediately thought of. Richard Belzer has apparently played the same character, Munch, on 10 different series as a result.
In the episode where Paul goes to get his remaining stuff from his old apartment from Kramer, he asks about the neighbor across the hall and gives a look to indicate that he didn’t think much of Jerry. (Don’t know how Paul would know Jerry since Kramer/Kessler was already living there when Jerry moved in.)
In one of the last episodes of MAY, Paul (on Viagra no less) runs into the “real” Jerry Seinfeld on the street and clearly idolizes him. So apparently there existed two different Jerry Seinfelds in the MAY universe. Both comedians. One Paul liked and one he didn’t. One in a crossover (but not seen). One in a guest appearance.
Dharma and Greg Montgomery showed up as prospective buys of the late Charlie Harper’s house in season 9 premiere. Either their marriage really went down hill in 9 years, or they’re still into bizarre public role play. Jenna Elfman previously played a different (though very Dharmaesque character). Joel Murray was in the same episode, but not as Pete Cavanaugh.
There was “The Springfield Files”, the episode of the Simpsons on which Scully and Mulder of the X-Files appeared.
A crossover that never happened but would’ve been nice to see:
Donald Bellisario, producer of Quantum Leap, wanted to do an episode in which Sam Beckett leaped into Tom Magnum, from Magnum, PI, which Bellisario had also produced. It would have established Quantum Leap and Magnum, PI as being in the same universe, and presumably Tom Selleck and John Hillerman, at least, would have made appearances in the episode.
Just last month there was a crossover with the Disney Channel shows Jessie and Good Luck Charlie. They called it Good Luck Jessie. Jessie also crossed over with Austin & Ally (Austin & Jessie & Ally).
There were a few episodes of “The Golden Girls” that touched on “Empty Nest,” mostly having to do with the dog “Dreyfus.”
One episode of “The Middle” included Ray Romano meeting Patricia Heaton, both playing different characters, including a “Don’t I know you from somewhere?” line.
There was a MeTV promo with Mary Tyler Moore (from the MTM show) watching the younger Mary Tyler Moore (from DvD) on a TV. They also have similar promos featuring Betty White and Ed Asner.
But there’s also an episode of Seinfeld where George watches Mad About You with his fiancee. So apparently there are two different Paul Buchmans in the Seinverse, one of whom used to live across from Jerry and one of whom is a fictional character in a TV show. And the real Paul and the actor who plays the fictional Paul look exactly alike.
Friends had a blackout in an early episode, could it have been that one? Chandler was trapped in a vestibule with some person named Jill Goodager whoever that is, while everyone else was looking for a lost cat or some such.
Speaking of Friends, a few years later NBC had “crossover night” where Jamie Buchman and her friend (Fran? I haven’t seen MAY in ages) showed up in Central Perk, and mistook Phoebe for Ursula. Meanwhile Ross showed up on The Single Guy that same night. I don’t remember the rest of that night’s crossovers, though.
ABC did a similar thing one night, with characters showing up in other show, all with Vegas involved. In particular, I remember Coach’s Luther character interacting with someone from the Drew Carey Show.