Mr. Centipede in James and the Giant Peach the 1996 Tim Burton film, is hated and abused by all the other bugs all the time, particularly by Mr. Grasshopper. By the middle end of the movie, the other bugs turned on him because they counted on him to lead the way to New York after he bragged that he had been there before, but he failed because he fell asleep and lost a sense of direction.
Hubie the Adelie Penguin from the movie, The Pebble and the Penguin.
Manolo from The Book of Life. Imagine if you were shoved into something you had no interest in, while everyone in your family AND village spat on your true ambition. And to make it worse, you're tricked into suicide because two gods placed a bet to see whether you or your best friend/love rival would marry the girl of your dreams and the god betting against you is a Sore Loser of the highest order. At least it gets better.
Other Wybie is mute, but very polite and friendly. The Other Mother sewed his face into a permanent grin when he frowned, and he still helps Coraline. It's implied that he was killed for this, with his awesome coat being hung on the house like a sick victory flag.
Other Father wasn't mute, but he was a very upbeat dude and just plain sweet guy. He's steadily being punished for trying to help Coraline, is beaten up by his own piano, and is forced to fight Coraline, trying his best to hold himself back so she can run, all while shouting "I'm so sorry, don't wanna hurt you!" in a disoriented voice. Falls into a bottomless pond and drowns near the end of the film, though the drowning at least allows him a Heroic Sacrifice ending, as he throws Coraline one of the objects she has to find to win against the Other Mother as he's going under.And the Other Mother makes him slowly mutate into a pumpking-thing. Seriously!
The ghost children could count. They were lured away from their homes, had their souls stolen by a monster and were locked up in a closet for decades, forced to live with the knowledge that if they hadn't given in to their greed, they wouldn't have been trapped.
Coraline herself counts, as her parents never have any time for her and she clearly really misses her friends back home. The Other Mother preys upon her loneliness and resentment of her parents to create the "perfect" world in an attempt to make her want to stay forever. When Coraline resists, the Other Mother kidnaps her parents, dismantles Other Wybie and nobody in the real world believes her, leaving Coraline alone and with no idea where her parents have gone.
The title character of the Korean short film Doggy Poo. It spends most of the movie pondering its purpose in life and crying its little eyes out. It does get a happy ending where a dandelion sprout asks to be fertilized by it.
Po in Kung Fu Panda starts off a bit as a Butt-Monkey in the first movie, but later in the movie when he shows just how insecure he is about being the Dragon Warrior, or how doubtful he is about being anything more than a noodle maker's fat panda son, you start to realize he had to go through a lot of crap for most of the movie. Sure, he gets to meet his idols, The Furious Five, but Shifu and them treat him awfully just about the entire movie. During those scenes you just want to hug him, and cheer for him as he gets up again and again even after all the hits and insults thrown at him. The sequel also has moments where you just want to hug him. First off there's how bothered he is about how he doesn't know what happened to his real parents, and the flashbacks he gets with Shen. Then comes when he finds out that Shen slaughtered all the pandas in China, and Po has to come to terms that he's probably the only Panda left in the land. But you find out at the end of the movie that his father and other pandas are still living somewhere.
The Land Before Time: Littlefoot, anyone? No one should have to watch their mom die before their eyes like he did. The scene later on where he's crying in her footprint just makes it worse.
And then there's poor, poor, Petrie, as lampshaded by the characters.
Sally. All the things she does for someone who doesn't seem to (at first) return her feelings is heart-breaking. Add in that she's The Cassandra and has an unhappy home and she's definitely a woobie.
Jack himself is one too. A guy who gets tired of his job might sound whiny, but not when you consider that he lives in a town where it's all about said job. Put that on top of the fact that a lot of the responsibility for Halloween is on his shoulders, and all you have to say is "That's rough, buddy". Also since Jack is Dem Bones he might be Really 700 Years Old, who knows how long he was doing the same thing every year. 10 years? 50 years? 100 years? Since Halloween was created? And he's also the biggest in-universe celebrity. That's got to be exhausting.
Michelle from Once Upon a Forest, who falls into a life-threatening coma after being exposed to chlorine gas. She does recover, but finds out shortly after that her parents weren't so lucky.
Norman in Paranorman. He's just trying to fix everything, is way over his head, and most of the town ostracizes him. Seeing him receive what is basically a No-Holds-Barred Beatdown from Agatha with electricity is really heart-rending.
Emmet. He's a very friendly guy but then the fact that a lot of people he considered friends don't really care much about him or even remember who he was. No wonder he wants to be special.
There's also Unikitty, as she watches the destruction of Cloud Cuckoo Land.
Private in Penguins of Madagascar. For what we know, his family lost his egg and didn't attempted to look for it. And that's just beginning! He was totally unappreciated by other members of team, then he was captured by Dave and had to watch his adoptive brothers getting mutated into monsters. Combine this with his Nice Guy personality and cuteness and you got A-Grade woobie.