Invader Zim: Miss Bitters, Dib and Zim's supernatural monster Sadist Teacher is implied in several episodes to have once been a happy little girl caught in a freak accident. Or a fairy princess who was hit by a bug zapper.
John Dee, a prison inmate with delusions of grandeur in the Justice League episode "Only a Dream", follows this trope when he becomes Doctor Destiny. Batman, being Genre Savvy, investigates him precisely because he is a nobody.
Green Lantern: Whatever he (Dee) is, he's not in the same league as Grundy and the others. He's a nobody.
Batman: Ever read the Odyssey? After Odysseus was caught by the Cyclops, he told it that his name was 'Nobody', so when he poked its eye out and his friends asked who did it all the Cyclops could say was "Nobody."
The same episode gives us this dialogue, with Dee's literal transformation From Nobody To Nightmare:
Dee's wife: John? What are you doing here? Get out!
John Dee: Y'know, I never liked that name. It's so... ordinary. Especially for someone with such big things in store. You know, a destiny? Ooh, I like that. DR. Destiny. What do you think?
Dee's wife: I think you're crazy!
John Dee (transforming into Dr. Destiny): Maybe. Or maybe you're just seeing the real me. And now that I'm a doctor... (turns into a grinning skull) I think I'llperform some surgery.
Another Justice League example: David Clinton, an inventor from the Batman Beyond era who appeared in the first season finale of Unlimited. After single-handedly creating a time travel suit, he started building a collection of historical artifacts. At first, he only took things that wouldn't be missed, but after spending six months as the prisoner of a Wild West thug he went flying off the deep end. He used technology from the future to make a League-killing army of the Jokerz and filled Gotham with stolen landmarks from other time periods, polluting history so much that time itself started unraveling.
Wasp, of Transformers Animated, started as just another Autobot recruit, albeit a bit of an asshole. Then he got framed for espionage and went insane in the stockade, before breaking out years later with vengeance on his mind. And after that, Blackarachnia gets her hands on him and mutates him into the techno-organic Waspinator, which leaves him with uncontrollable electrical powers and makes him even crazier.
This one's a bit of a meta example, too. There was another, very similar Waspinator in an earlier Transformers series, Beast Wars... But that Waspinator was was The Chew Toy.
Until Beast Machines, where it's revealed his spark was used to create the much more competent and dangerous Thrust, the longest-lasting and most dedicated of Megatron's Generals.
Optimus Prime in most continuities is a heroic example. His origins include being a dock worker, a washout cadet on a repair crew, or a data clerk. The Decepticon uprising forced the humble Orion Pax to reluctantly become the hero Optimus Prime.
The Transformers Prime version of Megatron was once just a simple Gladiator, in the harsh pits of Kaon. That simple warrior, would eventually plunge a planet into darkness and destruction.
And before that, like his IDW counterpart, he was a miner, this one a victim of Cybetron's corrupt caste system and a nobody who didn't even have the luxury of a name.
If the series continued, this trope would apply to Harry Osborn.
Hydro-Man in Spider-Man: The Animated Series. According to him, he was a "nobody" and was expelled from school for causing a lot of trouble. His parents sent him to the navy where he'll straight up. During a voyage, he accidentally fell into ocean where some strange mist from a fissure which "turned [him] from a nothing... into a something!"
Numerous TAS villains fit. The Hobgoblin was a petty street thug who was granted superpowers by Norman Osborn and turned into a lethally dangerous Psycho for Hire. Venom, aka Eddie Brock, was a failed reporter, before his accquisition of the alien symbiote turned him into one of Spider-Man's worst enemies (his successor, Carnage, averts this, as Kletus Cassady was a Mad Bomber long before he got his symbiote). And then there's Spider-Carnage. Take a badly unhinged kid. Give him Spider-Man's powers. Then, after a long bout of emotional trauma involving clones and an identity crisis, attach the Carnage symbiote to him. Hello Omnicidal Maniac.
In Teen Titans Johnny Rancid was the lowest tier criminal to ever appear; just a violent jerk with a motorcycle and a small laser gun. Then he gets the power to rewrite the rules of reality and turns the world into a gothic hellscape.
Willie Watt was a nobody who was picked on by the jocks and shunned by all the girls until he was given a visor to control a mini-Kaiju-sized, remote-controlled robot by his overly-aggressive and never satisfied father to fight back with. Willie then donned the visor and essentially went crazy because he was drunk with power and succeeded at getting back at the people who bullied him until Terry/Batman intervened, destroyed the visor and short circuited Willie's brain. Then at the end of the episode with Willie in juvenile, he found out he had gained psychic powers. THEN on a episode in the next season, Willie was released from juvie with a noticeable change in appearance (i.e. buff) and started getting his respect and trying to take Blade, the girl who had rejected him before. Now he was a jacked up, psychotic psychic Somebody.
Then there's Shriek. He was once Walter Shreeve, a phonologist, sound studier, and engineer. But when he was told his funding would be cut, Derek Powers offered to let him continue if he would kill Bruce Wayne. After his initial battle against Batman, Shriek lost his hearing and began using his powers like any supervillain. And he was one of the more dangerous ones that Terry had to face; at one point, he put a Curse of Babel on the whole city in an effort to get them to hand over Batman to him.
Ira Billings would come to be known as Spellbinder. He was at first a bitter and underpaid psychologist at Terry's school. To gain some cash, he used his self-made VR technology to get students to steal for him. After being arrested and escaping, he began making even stronger VR simulators giving runaways and unwanted kids a perfect life for a short time in exchange for stealing, knowing they would overdose in time and didn't care. He also got a city-wide manhunt going against Batman by making people think he killed one of his Rogues Gallery in cold blood.
Wakfu: Noximilien Coxen was an unassuming watchmaker and a family man. Then he accidentally got his hands on a little something called the Eliacube...
Wrath-Amon from Conan The Adventurer used to be an ordinary Gila monster. After Ram-Amon used the Black Ring to turn him into a lizard man, Wrath-Amon stole the Black Ring from him and took control of the cult of Set.
Thanks to the Nanite event in Generator Rex, every living thing on Earth (except White Knight thanks to a near-lethal accident) has the potential to become a horrible monster. The first EVO threat seen in the series was an ordinary guy who spontaneously transformed into a several stories tall Kaiju that only The Hero Rex (a more advanced EVO) can defeat without nuking the area.
Special mention to Van Kleiss, who was a minor lab technician at the facility that invented the nanites before the event, and is now a Magneto / Orochimaru hybrid leading the largest organized group of malevolent EVOs.
Alpha from the Heroes UnitedCrossover was a freaking Nanite that eventually became a menace capable of destroying the entire world.
The Lich is heavily implied to have once been an ordinary person before the Mushroom Bomb's fallout mutated him into an undead monster.
The alternate universe of Danny Phantom if you think about it. The title character was an average unpopular kid who suddenly gained super powers and became the local super hero, only to lose his humanity in an attempt to dull the pain of losing his friends and family, and willfully caused The End of the World as We Know It.
Bolero has an evil, black eyed monkey who starts off as a shadowy figure before eventually becoming a towering man who kills off all the animals, thus halting evolution.
Kyle: Dude, I don't think we should piss Cartman off again from now on.
Stan: Yeah, that's a good idea.
The Legend of Korra's Amon was a young waterbender named Noatok, until his father, a former criminal, forced him and his brother Tarrlok to learn bloodbending. After years of such training, Noatok was fed up with it and ran away from home, convinced that all bending was evil, even implying that he contained self-loathing for being a bender. He would eventually form the Equalists, who sought to rid the world of benders, and tore Republic City apart, socially and politically.
Trixie was a loud egotist whose boasts way exceeded her actual power level, a foil to the immensely powerful but humble Twilight Sparkle. After her home got destroyed and she got laughed at by the whole of Equestria, she acquired a powerfuland corrupting artifact, which let her trounce Twilight and enslave Ponyville. She gets better by the end of the episode, once the heroes manage to remove it from Trixie's possession.
Zoltan and the Gang of Five from Attack of the Killer Tomatoes! were comic relief sidekicks in season one until they mutated into serious threats in the second season and succeeded in taking over the world.