There's an episode of Frasier that has a brilliant opening sequence that has nothing to do with the rest of the episode. Niles is using Frasier's apartment to cook dinner for a date. Everything is perfect, but while he's waiting for his date to arrive, he decides his pants need to be pressed, so he gets out the ironing board and starts to iron his pants. Then he sees a loose thread, and cuts it off, but cuts his finger in the process. He sees the blood and faints for a moment. When he comes to, he realizes that he got a blood stain on Frasier's leather sofa. He get some spot cleaner to get out the stain, but sees the blood, passes out again, and spills the cleaning solution all over the sofa. One thing leads to another and it ends up with him setting the couch on fire, ruining dinner, and passing out on the floor. Part of what was so impressive about this scene was that there were very few cuts and it was all filmed pretty seamlessly.
There's an episode of Mad About You where Paul has a series of bizarre dreams that ultimately take the form of the dance sequence from Rowan & Martin's Laugh-In.
There's an episode of Friends I like to think of as the "alternate universe" episode, which shows us what the friends would be like if Monica were fat, Joey was a successful actor, Chandler was an unemployed writer, Ross and Carol were still married, and (my personal favorite) Phoebe was a super-bitchy Type A stock broker.