The eponymous character of Megamindclaims to be this. But he's actually quite lacking in the woobie part and even more so in the destroyer of worlds part.
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.
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.
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 Guardian takes 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. Averted with Jack Frost, who remains happy and joyous, making kids happy despite having no one believe in him.
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.
Films — Live-Action:
In Chronicle, Andrew is bullied and made fun of constantly through the movie, in addition to a sick mother and an abusive father. After he gets his superpowers, he begins to snap, and starts to get involved in crime to save his mother's life, stealing medicines and such. By the end of the movie, during the climax, he nearly destroys the city.
Milton (Stephen Root) in Office Space. After enduring bureaucratic neglect, managerial indifference, and stapler deprivation, he walks into the Initech office complex, finds and steals an envelope full of embezzled cash, and burns the place down.
The eponymous character of Carrie 1976 is certainly a Woobie, Destroyer of Worlds, even if she doesn't quite want to destroy worlds... just most of her high school. Her rampage luckily ends before she gets the chance to do anything more.
But only in the 1976 film. In the book and the remakes, she wants to kill everyone at her school, everyone in her town, and everybody else. Fortunately, she dies before she can commit anything more than demolishing her school, giving her mom a heart attack that kills her, killing two horrible bullies in a car crash, electrocuting several people, and setting her town on fire.
Spoofed in the zany teen comedy Zapped!, in which science nerd Barney Springboro is similarly degraded at a prom when the Alpha Bitch throws a watermelon at his head, almost knocking him out and causing almost everyone in attendance to laugh at him. Barney avenges himself by using his telekinetic powers to blow open the gymnasium doors and summon a hurricane-like wind that strips everyone except Barney's prom date and his best friend down to their underwear. Woobie, Nudifier of Worlds, perhaps?
The Moorwen!!! In Out Lander, its species is destroyed for being less intelligent than man, and its only offspring is killed off brutally. You should give it a hug...if you believe you won't get torn apart.
Ramon from Alligator counts as this to an extent.
J.D. (Christian Slater) in Heathers. For starters, his father is a sociopathic bastard who doesn't care for him (when asked if he even likes his father, he responds that he "[hasn't] given the matter much thought"), and his mother killed herself in front of his eyes to get away from her husband. His entire life was spent moving around from town to town and school to school wherever his father's demolition job took him, where, it is implied, he saw the same scenario of clique groups bullying other students at every high school he's attended. He starts out by murdering Jerk Jocks and Alpha Bitches and making their deaths appear as suicides (also implied as something he's done before), but he ultimately resorts to trying to blow up the entire school. He explains his intentions are such because he believes that nobody loves him, and that "the only place different social types can genuinely get along with each other is in heaven", somehow seeing the school as a representation of society itself.
Bartleby in Dogma: he eventually snaps, realizing that God always favored man above angels like himself, gives up hope that "He" will never forgive him and Loki for their menial transgressions, and so decides to kill everything.
Davy Jones from Pirates of the Caribbean doesn't seem to want to destroy everything - just everything that crosses his path. He's like this because his one true love, the goddess Calypso, betrayed him (presumably for another man, though it's never elaborated on) centuries ago. Jones' agony was unbearable, so he cut out his own heart to end it. When that failed, he adopted a different tactic - finding relief by sharing his pain with everyone he meets.
Oswald Cobblepot in Batman Returns: disfigured since birth, his aristocratic parents attempted to drown him in the sewers. He was found by a traveling circus, and was raised in the freak show as "The Penguin". While the public views him with sympathy, he has become a warped sociopath, plotting to murder all the first born sons of Gotham City. When Batman foils him, he straps rockets to his hundreds (thousands?) of pet penguins, intending to use them in a suicide bombing to kill all of Gotham, which, as the only setting we see, is extremely omnicidal in context. And yet, you still can't help but pity him at his death.
Grace in Dogville. Made all the more ambiguous by the discussion just before the ending, where it suddenly becomes very clear that she's only a child.
In a perfect example of Break the Cutie, Alessa Gillespie from Silent Hill was burned alive by the cult she was a member of, but survived by her own power and remained wrapped in bandages for 30 years, unable to move anything but her eyes (and her lips, but only enough to kind of smile, but not enough to form words). She does the only logical thing and splits her soul into 3 parts so she can kill everyone in the cult (excluding Rose, her good half, Sharon, and her mother).
Gurdy the Clown / Luther Edward Baxter from 100 Tears.
May is a particularly heartbreaking-cum-vicious example.
The infant(s) of It's Alive, whose homicidal rampage turns out to be birth trauma and separation anxiety, and who longs only to be reunited with his family.
Sadako in Ringu and her counterpart, Samara, in the US remake, The Ring, considering that both were mistreated and murdered.
Asami in Audition. She endured a horrific childhood.
Eli in Let the Right One In, a vampire who is trapped not just physically in a 12 year old body but apparently emotionally as well, forced to kill to survive, whose only friend is an equally screwed up boy.
Also, Abby in Let Me In, the remake of Let the Right One In.
Bill Foster in Falling Down goes on a rampage of terror after his wife left him and would not allow him to see their daughter. He is fired from his job in the defense industry due to post-Cold War budget cuts and is generally just pissed off with the state of the world and takes his anger out on every issue, whether minor (foreign shopkeepers, high prices, poor fast-food service) or major (racism, social class, unemployment). While he is overly violent, he is representative of the everyday man pushed too far by the world.
Loki in Thor. He wanted to prove that he was just as good as Thor, and then found out that he was descended from Frost Giants, after being raised around Asgardians who hate Frost Giants. He's also Laufey's son. He believes that he never really had a chance because Odin would never want a Frost Giant on the throne. He was passed over in favor of Thora lot during their childhood. He takes a more literal turn in the film's climax when he tries to use the power of the Bifrost to destroy Jotunheim.
In the subsequent The Avengers, Loki has become the main villain and attempts to subjugate the entire population of Earth.
And in the sequel to Thor, Thor agrees to let Loki out of prison in exchange for his help against the new threat to Asgard.
Oddly enough, Michael Myers is one of these in the Halloween (2007) remake. Director Rob Zombie tried to portray him in a much more sympathetic light.
From the rebootseries, we have Nero and John Harrison/ Khan. The former was a Romulan miner who tried saving his homeworld from being destroyed by a supernova, only for the galactic bureaucrats to dismiss him and becoming driven insane with grief and a thirst for vengeance against Spock, the man who promised to save his world. The latter ,while an Evil Overlord back in the day, just wants to save his crew from Admiral Marcus, who forced him into making weapons for the Federation at the risk of having them killed. Harrison even calls them his family and starts tearing up about how he couldn't save them.
Godzilla. The original film shows him as a Tragic Villain, just as much a victim of nuclear weaponry as anyone else. This is especially evident in the Heisei films, where he's portrayed as more of a "force of nature" rather than an outright villain.
Elijah Price in Unbreakable is afflicted with Osteogenesis Imperfecta, which creates a brittleness in his bones that make them very susceptible to fracture. He can't do things other kids can do in his childhood, is constantly in casts, and only has comicbooks to bring him joy. Then he decides that his purpose in life is to be a supervillain...
John Harrison/ Khan Noonien Singh in Star Trek Into Darkness. He may be a bit of an asshole, as well as a ruthless killing machine, not to mention an Evil Overlord at one point, but he's been frozen for 250 years, then turned into a killing machine by the Federation, then tried saving his crew only for Admiral Marcus to take them away from him once again. It's a bit hard not to feel sorry for him.
Harrison: My crew is my family, Kirk. Is there anything you would not do for your family?