Mulan II derails several characters: in addition to giving Mushu Aesop Amnesia and making him a bigger jerk, Mulan and Shang start arguing using sex stereotypes as insults, and Chien Po goes from a Gentle Giant who loves to eat to a flat Fat Comic Relief character who is Obsessed with Food (and engages in pointless brawls, something he pointedly did not do in the first movie). But the character who got it worst was Ling, whose personality got traded in for... wanting someone to laugh at his terrible jokes. This becomes his motivation despite not even being hinted at in the first movie.
Pocahontas II derails many characters as well. Pocahontas herself became cold and distant, John Smith was changed into a wise-cracking self-absorbed Jerk Ass, Meeko fell victim to Aesop Amnesia (especially in regards to his friendship with Percy) and Racliffe became a Karma Houdini whose evilness went Upto Eleven.
The Little Mermaid II: Return to the Sea, which is very ironic, considering the title character becomes a parent! The first movie shows Ariel as being curious, open-minded, brave, and impulsive. The sequel gave Ariel a horrible case of Aesop Amnesia, causing her to make the exact same mistakes with Melody that Triton did with her. And that's not even counting the very stupid decision to keep Melody's heritage and background a secret from her, arguably giving her better reasons to be defiant than Ariel, who at least knew why her father had the rules he did.
Dr. Lawrence Gordon's long-awaited return in Saw 3D counts as this. This is considering the last time we saw him (in part 1), Lawrence was crawling away from his bathroom-prison, shivering from the blood-loss incurred from cutting off his foot and promising he'd find help for the still-shackled guy being tested with him (this is after he believes his family may well have been shot and killed due to his inaction in the "test"). In Saw 3D, he is a willing accomplice to John "Jigsaw" Kramer. In the first scene we see Dr. Gordon in during the present-timeline, he is delivering a cheesily villanous sounding monologue to the protagonist of the film, his smirking henchman demeanor majorly contrasting with the distrought husband/father he had become throughout the first film. Whatever real change occurred apparently happened completely offscreen, and what's more, apparently happened in the span of about 2 months, as we see Dr. Gordon smiling whilst placing a key behind a trap-victim-to-be's eye during a flashback that slightly predated part 2. At no point in Saw 3D does he mention his family or the guy he left behind, and ends up only looking at the latter's corpse rather dully during the climax when he returns to the bathroom.
An even better example is Jigsaw himself. Jigsaw made a huge point that he never killed anyone, merely put them in position where they had to fight and occasionally compete to live. Then in Saw VI he suddenly was fine with using Hoffman's traps, which did kill people outright.
They didn't kill people outright any more than Amanda's trap in the very first film did, or Gordon's test as intended. Come Saw 3D he has no real such excuse, as the final trap is impossible and kills Joyce out of spite rather than as a result of Bobby's own failure. Add this on top of the aforementioned Gordon example, Jill's severe Chickification, and Hoffman's Flanderization into an Ax-Crazy slasher villain, and everyone got derailed in this movie.
It's worth remembering that Jigsaw did mortally wound a police officer with a concealed dagger during the first film, and there was no way that innocent man just doing his job could have "earned" his survival from that attack. His moral stance can seem more of a pretense for his actions rather than a motive when you take that into account.
Purposely done in the case of Susan Orleans in Adaptation. Portrayed as simply a reporter who develops a bond with John Laroche, due to Charlie Kaufman's in-story Creator Breakdown she proceeds to become a psychotic drug-addict who regrets her life.
Unfortunately, Falcor also got this treatment in the third movie. He was a wise, gentle creature that would gladly lend a helping hand, but in this one, he's the dragon equivalent of Scooby-Doo.
Norrington in the Pirates of the Caribbean movies. In the first one, he is Will's rival for Elizabeth's affections and, as a naval officer, hates pirates and is out to get Will and Jack. But he's far from a bad guy, takes it gracefully when Elizabeth chooses Will over him, and gives Jack a Mercy Lead at the end. When he comes back in the second movie, suddenly he's a bitter drunk with a grudge against Will for getting the girl and Jack for escaping and ruining his career, and he becomes a pirate himself. The third movie tries to reconcile these two portrayals and treats him a bit better, but Redemption Equals Death and he gets killed off rather abruptly.
This didn't go entirely unnoticed in the second film, however; he mentioned that the reason he lost his career and went drunk was because he lost his ship and got his entire crew killed in a hurricane he only got caught in because of the Mercy Lead from the first film. Survivors Guilt was heavily implied.
Michael Corleone. Compare this character between part III of The Godfather and the rest of the series. In the first two parts he was a dead-serious and moody fellow. In the final sequel he's got cute quirks and snarks.
Jim Phelps in the first Mission: Impossible. Fans of the TV series were not happy when he turned out to be a traitor who sold out his own team leading to almost all of their deaths. Peter Graves even refused to reprise his role because he felt that it completely betrayed Phelps' character.