Danny from Cats Don't Dance: He arrives to Hollywood with big dreams and is met with nothing but scorn and cynicism from every other character. He doesn't break, he instead rallies the other animal actors until he rekindles their own dreams.
Chirin No Suzu. Chirin loses his mother to the Wolf King. He spends the rest of the movie corrupted by his own desire for revenge. It doesn't end well.
5 from 9 is a very sweet and trusting character, but that doesn't stop him from getting abused. First he loses his eye. And then his best friend is killed right in front of him. And then, right when it seems like everything is going to be all right, he dies.
The normally cheerful and adorable little she-squirrel in The Sword in the Stone is tragically left heartbroken and in tears when Wart is turned back from a squirrel into his human form.
Arguably, WALL•E. Let's see, the main character gets rejected by his love, multiple times, and ends up risking his life to help her; said girl is called dysfunctional, is classified a rogue robot, and watches the robot she finally loves get squashed; and that's not counting the myriad of possibilities in the repair ward. He's still a pretty cheery guy.
James and Hilda Bloggs of When the Wind Blows are a nice retired British couple who could be your grandparents. They really don't understand the implications of surviving World War III, so we're going to see them die of radiation poisoning, still believing that the Government will collect them.
Susan Murphy of Monsters vs. Aliens. Hit by a meteor on her wedding day, she begins glowing green and turns into a monster, sending everyone she knows fleeing in terror. She's captured by the military and locked away permanently. She's with real monsters who don't understand her. When she finally gets a chance to get out (by facing something out of her nightmares), her fiance rejects her and she's abandoned. Then she's kidnapped by an alien who wants the phlebotinum that turned her into Ginormica so he can destroy the world. She finally grows a backbone and takes a level in badass.
Simba of The Lion King was once a fun-loving and somewhat immature little lion cub who just couldn't wait to be king. Then the poor kid is trying to get his father, Mufasa, to wake up after his evil uncle Scar sent him off a cliff to be trampled to death by a wildebeest stampede that his hyenas set off in a dastardly scheme to take the throne of the Pride Lands for himself. Just for added Kick the Dog measure, the son of a bitch then makes Simba believe that he was responsible for his father's death before then encouraging him to leave the Pride Lands and never return, while at the same time sending his hyenas to kill him. It takes a number of years with Timon and Pumbaa, a reunion with his childhood sweetheart Nala, and a fateful meeting with the ghost of his father before he's finally ready to take back his home, and it was only after learning the truth of who was responsible for Mufasa's death that he truly manages to turn things around emotionally.
Bambi. He loses his mother and has to live with someone who doesn't seem to care about him at all. He gets better.
The Fox and the Hound. Tod and Copper, who evolve into a Woobie and a Hero Antagonist through the course of the film. They start out as best childhood friends, and one of them is supposed to kill the other. Tod especially gets it bad; he is abandoned by the only family he knows to live in the forest where he meets some angry critters. He falls in love with a girl fox and makes a fool out of himself in front of her. His best friend blames him and wants to kill him for something that wasn't his fault. The way he got his friend to forgive him? Fight a giant bear and nearly die. And it's implied that they aren't allowed to see each other anymore after that.
Happens to Mater in Cars 2 after he discovers that everyone else views him as a clueless ditz, good only at distracting others while real heroes get things done.
The Powerpuff Girls send themselves on a self-imposed exile after becoming pariahs in the eyes of Townsville and even the Professor. As they commiserate on a lone asteroid, Blossom stares up at the earth with tear-filled eyes, buries her head in her hands and cries to herself.
Vanellope Von Schweetz from Wreck-It Ralph gets this treatment quite a lot. She is persecuted by the other racers of Sugar Rush, her game world, and not allowed to race as she is glitchy and clumsy and players may think the game is broken if she glitches when being played, which may cause the arcade to "unplug" the system (which would mean something of an apocalypse to the game's inhabitants). As an outcast, Vanellope lives alone in a secret, unfinished level; a volcano full of soda and dangerous pop candy. She also has no memory of her past, only that she knows 'racing is in her code', despite never setting foot on a race track. Meeting Ralph helps her cope with this, as they are very much alike in that they exist but don't get enough love from their peers.
Both Vanellope and arguably Ralph himself go through a straighter breaking later, after King Candy convinces Ralph to wreck Vanellope's kart for the good of both herself and the game as a whole - all part of the main villain's plan, as he had messed with the programming with only his own interests in mind. Ralph was only able to un-break Vanellope after he realized that something was amiss in the first place, due to her picture being on the side of her game console.