The Toad from Flushed Away. He was once Prince Charles' favorite pet. Then someone brought in a rat and flushed the Toad down the toilet so Charlie could focus all his attention on the replacement pet. This became his motivation for attempting to wipe out the Sewer-London. Seriously, we can't blame him for what he is now.
Ice Queen Elsa from Frozen is more of an angry loner than anything due to years and years of having to control her emotions and powers, only to have it amount to nothing. And the "Destroyer of Worlds" part is unintentional.
Shen of Kung Fu Panda 2 might count as one if the audience takes into account his official biography. Considered too weak and sickly to warrant his parents' attention, Shen was left to the care of the Soothsayer. He strove to earn his parents' approval and ended up discovering the explosive potential behind fireworks. When the Soothsayer foretold his defeat at the hands of a warrior of black and white if he continued down his dark path, Shen slayed the pandas, believing averting his fate would finally earn his parents affection. They instead banished him and Shen saw this as the final sign that his parents did not and would never love him. He spends the rest of the movie killing and destroying out of a desperate need to fill the void in his life, knowing full well there is nothing he can do to make himself happy but also knowing there is nothing he can do to justify his actions. Worst of all, the only reason he goes forward is because to turn back would mean everything he did up until now would be for naught. No wonder he seems to find peace when in the final battle something falls on him.
The Once-ler from the 2012 The Lorax, big time. His drive to create his Thneed business is largely due to his jeering, un-supportive family. When the business takes off, he becomes carried away with his success, and is corrupted by greed and power, becoming as big a Jerkass as the rest of them. Once the entire forest is destroyed, however, he realizes what he's done, as well as the fact that he's now ruined.
The eponymous character of Megamindclaims to be this. But he's actually quite lacking in the woobie part (compared to other more broken and less humorous examples at least) and MUCH more so in the destroyer of worlds part.
Bowler Hat Guy (aka Michael 'Goob' Yagoobian) in Meet the Robinsons. The best friend/roommate f the main character, he is a gloomy boy who has endured alot of the shanngians his friend caused, but after being blamed for losing a game (due to falling asleep since he's often kept up, he's consumed by bitterness and becomes a bitter adult who never got adopted and became a pawn in a bigger scheme.
At the climax of My Little Pony: Equestria Girls – Friendship Games, the human Twilight Sparkle, having come from a Friendless Background and been ostracized by her classmates, gives in to peer pressure to "Unleash the Magic" she has gathered from the Humane Five with her amulet, which transforms her into "Midnight Sparkle", a raging she-demon even worse than Demon Sunset Shimmer, and proceeds to tear apart the dimensional fabric between the human world and Equestria, threatening the destruction of the former if not both.
Aggie in ParaNorman. She was executed as a child after being accused of being a witch. Her spirit becomes angrier with each passing year, ultimately releasing her rage in the film's climax.
In Penguins of Madagascar, Dave's sole reason for becoming an evil mastermind is due to the fact that that he feels penguins stole his glory at every zoo and aquarium where he was ever an attraction.
In Rise of the Guardians, Pitch Black, AKA the Boogeyman (as especially revealed in the prequel novels), believes that the fear he embodies is necessary, and that the approach the Guardians take is foolish. But, since he hasn't been believed in for centuries, thanks to them, he tried to destroy everything they represent, just showing that his bitterness has destroyed any decency he once had. And when he tries to reach out to fellow loner Jack Frost, he is brushed aside. The look on Pitch's face says it all.
Averted with Jack Frost, who remains happy and joyous, making kids happy despite having no one believe in him.
In Toy Story 2, Stinky Pete, the prospector, spent his whole life on a dime store shelf, watching every other toy be bought by kids. This agonizing experience caused him to become bitter and willing to manipulate or outright force his "friends" Woody, Jessie, and Bullseye into going along with what he wants, whether they like it or not. Ironically, when he winds up being taken home at last by a little girl who defaces all her toys by drawing on them with crayons, he considers this the worst fate imaginable. However, according to the producers, it was stated that he accepted that fate and thus, averts the worst fate imaginable.
Big Baby in Toy Story 3 is also this. He's the scariest villain ever- until this:
(Looking at tag saying "My heart belongs to Daisy") *sob* Mama?
Lotso in the same movie also has a Woobie-ish backstory, but it's made pretty clear by his actions both prior to and during the movie that he abandoned the 'Woobie' part long ago.