Ok, this may not fall under the category of "Movies that Shouldn't Have Sequels", so much as it does "Movies that Should Never Have Had Sequels."
The Lion King should have ended with the first movie.
Lion King 1/2 was (to me) enjoyable.
It wasn't as amazing as the initial film, but it was a nice movie (and anything is an improvement over 2).
The Lion King 2 should die. Slowly and painfully. It is my least favorite movie ever. Star Trek V is better than this, if only because in that you get to hear Leonard Nimoy's voice.
The only good bits were Timon and Pumbaa, probably because they're Timon and Pumbaa.
And don't get me started on the songs, I would say that I could rant on them til the end of days, but all my feelings on these horrid abominations of musical garbage can be summed-up in three little words: I. Hate. Them.
Sorry for the long rant, but I've never before had the opportunity to properly rip into these movies.
As for "What Probably Shouldn't Have Sequels": Big Hero 6 and Frozen.