Ramon from Alligator counts as this to an extent. Flushed down the toilet and abandoned in a sewer all his life before he grows into a big friggin' gator with an appetite for humans.
Asami in Audition. She endured a horrific childhood.
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.
Candyman: Candyman became an undead monster after he was murdered by a lynch mob because he was a cultured black man who fell in love with a white woman in the 19th century.
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?
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 money for her medicine and such. By the end of the movie, during the climax, he nearly destroys the city.
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.
Bartleby: We're going home, Loki! And no one, not you, not even the Almighty himself is going to make that otherwise!
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.
Eve of Destruction: EVE III is somewhat of a tragic villain in that she's mostly just confused and kills people who she thinks have either wronged or upset her while believing that she's the real Dr. Eve Simmons. It's not even clear if the robot itself is aware that the nuclear device inside it has been triggered at all.
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.
Also a Decontruction of the trope, as his police officer counterpart, Prendergast, is experiencing similar bad fortunes, with co-workers who don't respect him and can't wait to usher him off to retirement, a wife who walks all over him, and a general sense of fatigue for most of the film. However, he doesn't break, and in fact, delivers a beautiful The R Eason You Suck Speech to Foster.
Fantastic Beasts and Where to Find Them introduces us to the concept of an Obscurus, which is a rare and powerful magical parasite that is the end result of a powerful magical child being abused and forced to repress their abilities until they can’t be contained anymore. At which point the resulting Person of Mass Destruction goes on a rampage destroying everything in its path, scared and angry after a lifetime of pain. A specific example would be Credence Barebone: He’s abused and controlled by his Fantastic Racist of an adoptive mother (along with his adoptive sisters, though he gets the worst of it), which has left him shy, deeply insecure and emotionally stunted. He has no friends besides his youngest sister Modesty and is mocked by the Shaws (particularly Henry Shaw Jr, who has no qualms about calling him a freak). This leaves him open to manipulation by Percival Graves/Gellert Grindlewald, who baits him with affection and the promise of teaching him magic so that the older man can use him for his own selfish reasons. And once Grindle!Graves gets what he wants, he has no issue throwing the poor guy away or calling him worthless. This leads to Credence hitting the Rage Breaking Point and willingly unleashing his Obscurus on New York City, which is as tragic as it is terrifying.
The original film shows Godzilla 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.
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.
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.
How the Grinch Stole Christmas!: As part of the film's Adaptation Expansion, the Grinch is given this treatment. He was adopted by two elderly Whos as a baby, and bullied for his appearance, particularly by Augustus May Who, the current Mayor of Whoville. During one Christmas season, he made a gift for his crush, Martha May Whovier, but after being made fun of for having a "beard" at his age, tried to shave his face, cutting himself in the process. When his classmates ridiculed him yet again for his shaving cuts the next morning, that was the last straw: he went berserk and went on a rampage, destroying the gift he made and throwing a Christmas tree across the classroom before fleeing to the top of Mount Crumpit, declaring his hatred of Christmas.
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.
Big Daddy from Kick-Ass is a rare heroic version when you find out what Frank D'Amico did to his life.
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.
Francis Dolarhyde from Manhunter (1986) and Red Dragon (2002): actually lampshaded by Will Graham; he says that he feels a lot of sympathy for the child he once was, but thinks someone should put a bullet in the adult Francis' brain.
May is a particularly heartbreaking-cum-vicious example.
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 Moorwen!!! In Outlander, 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.
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.
Sadako in Ringu and her counterpart, Samara, in the US remake, The Ring, considering that both were mistreated and murdered.
As we learn more of Darryl Revok's backstory in Scanners, it becomes increasingly apparent that he became a psychic supremacist with ambitions of world conquest due to all the abuse he suffered because of his supernatural abilities. He tranformed his inferiority complex into a superiority complex to cope with being called a freak and locked up in a mental asylum for years, as pointed out by Dr. Paul Ruth:
Dr. Ruth: At the age of 22 he was extremely self-destructive; now at the age of 35 he is simply destructive.
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).
Dr. Tolian Soran in Star Trek: Generations. His homeworld is destroyed by the Borg, causing him to lose his family. He then ends up in a Lotus-Eater Machine where (presumably) he's reunited with them, only to be torn away by people trying to rescue him. No wonder he gets obsessed with getting back what he lost.
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.
In Star Wars: Revenge of the Sith, Anakin Skywalker's final transformation into Darth Vader is shown to be caused by losing everything and everyone he cares for, albeit due to his own actions.
Kim Jong Il from Team America: World Police. He's plotting the destruction of society as we know it, but deep down, he's just "a rittre ronery" (read: little lonely).
Loki in Thor. He wanted to to show his father that his brother wasn't perfect, and then found out that he was a Frost Giant, after being raised by Asgardians to hate the Frost Giants as monsters. He's the natural son of his adopted father's greatest enemy. Convinced his family has never loved him and Odin only kept him alive for some ulterior purpose, he sets out to prove himself as an heir. He was passed over in favor of Thora lot during their childhood. He becomes a literal example in the film's climax when he tries to use the power of the Bifrost to destroy Jotunheim.
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...