There are two other shark-jump threads on other boards, but eh, I figure this one will be better.
As you probably all know, jumping the shark is when a show goes downhill. An example would be if X-Men Evolution was a decent show, but that Spyke kid came to town and made it the crap it was. That all said:
Gundam - the Backstreet Boys are recruited
Family Matters - it came extremely close to jumping with "The Rapping Winslows" and when Urkel took over the show, but it still made some sense, at least. But there was no redeeming it after Urkel's wacky inventions, like the split personality machine.
American Dad - first episode
Dragonball Z - Gohan becomes Greg Brady
Teenage Mutant Ninja Turtles - Red Sky season. Carter is the best example of a character making a watchable show jump shark.
Inuyasha - After the mansion fight with Naraku, when they end up right where they began, for the first time. Only difference is that characters like Ryoga get thrown into the mix.
Naruto - Sasuke is confronted, and then goes into a flashback.
Rave - Musica
The Simpsons - not sure, really. It took a few dives (Maude dies, Homer's IQ goes from 90 to 7), but I never stopped watching. Until, that is, I saw a skinny, competent Michael Moore guest starring.