Mariavel Varella, the primary villain of Survival of the Fittest v2, has something of a Freudian Excuse to justify her actions. She was raped by her father as a child (although this may have since been the subject of a Retcon). However, what does remain Canon is the other abuse she suffered at the hands of her father - as well as him killing her brother.
Steff in Tales of MU: "Don't you think I've earned a chance to be the one at the top of the shitheap for a while? Three more years and then nobody's going to fuck with me, ever again."
In Yu-Gi-Oh! The Abridged Series, Tristan asks Bakura why he is so evil, to which Bakura replies "Well, I guess my mummy didn't love me enough. Did you know she wanted to name me Florence? Who names a boy Florence?!"
Gaia Online's current Big Badwas neglected by his "father", Johnny K. Gambino, in favor of his natural son Gino. This led him to found his own Mad Scientist corporation, NeXus, to study the Animated and eventually use them to try and take over the world.
Lord Doom, an Evil OverlordWell-Intentioned Extremist supervillain from the Global Guardians PBEM Universe was nine years old when he became the only member of his family to survive internment in a Nazi concentration camp (his father was executed right in front of the boy by a camp guard who was "merely testing his newly-issued pistol"). He didn't even have the consolation of a community of Holocaust survivors to relate to as his family wasn't Jewish, or Gypsy, or Slavs... there were merely politically inconvenient. His campaign to take over the world is founded on his very real, very sincere, and very, very obsessive wish that no more children suffer the loss of their Mommy and Daddy and little sisters like he did.
Parodied in the Dragon Ball Z Abridged: The Christmas Tree of Might: Turles hates Christmas because Santa never visited Planet Vegeta, and so their only holiday was Freeza Day. Also his henchmen all did horrible things, including dropping a whole truck of coal on a naughty child's house and raping Rudolph.
Unsurprisingly, this is implied to be the reason RedLetterMedia's Mr Plinkett is a mentally unstable kidnapper and murderer. He mentions attacking a doctor who asked about his "dear old mother", then we are shown a brief flashback of his mother telling him to "bury the bodies under the floorboards".
Tom tries to be better than his younger brother, who was superior to him in every way since they were kids. As you might expect, this doesn't justify why he picks on Zack.
Zack's father dictates his life, so he's never had to make a decision before. That's why, when he begins working with Dana and Tom, he acts like a Manchild.
The Nostalgia Critic mentions that part of the reason he dislikes Doug is that when he was younger (when the show was popular) a lot of people would tease him about it and constantly bring it up, saying "If you were named 'Doug', you were ALWAYS associated with this show."
Souichiro's ghost possessing Aizawa (to Light): Shut up! I knew I shouldn't have pushed your mother down the stairs while she was pregnant with you!
Narrator: Mikami grew up in an abusive household. His father was a professional badger wrestler too busy on the road to come home. His mother had a rare disease that left her with no eyes or upper face and she drank to excess... And now your mother's dead. She died while you were still in school and it scarred you FOR LIFE!
In 'Let's Drown Out WWF No Mercy', Ben Yahtzee Croshaw revealed that the very reason why he does not like pro wrestling was because when he was a kid, his friends had gotten into trading collectible WWF stickers and essentially alienated Yahtzee out of their social groups. His commentary partner Gabriel summed it up pretty nicely:
Gabriel: WRESTLERS TOOK MY FRIENDS!
We have this with Toki, who, throughout numerous stories in which her backstory was mentioned, was noted to have been abused by her adopted mother, which lead to her seeing the world as she does (Toki was very naive at the time), giving her a fairly warped up sense of right and wrong, and causing her to develop mental illnesses. Amoridere did note here that it doesn't justify her actions, rather, it explains them.
Weiss of RWBY harbours a strong distrust of Faunas. This is because the White Fang, a terrorist group that fights for Faunas rights, has terrorised her and her family for years. The White Fang have kidnapped several of her friends and family, and it's implied that she was a victim of her father's temper brought about by the White Fang's actions. The thing is, a later scene reveals that Blake is a Faunas and a former White Fang member, as she blurts out after a heated argument. Weiss' Fantastic Racism is wrong, sure, but it's easy to sympathise with her if her backstory truly was that crapsack. The whole aforementioned scene is quite a tragic example of two victims of a very morally grey conflict butting heads.
Emerald and Mercury are both very nasty people, but their DarkAndTroubledPasts at least partially explain their behavior. Emerald grew on the streets and it seems like she was made very cynical and desperate by the experience. Mercury on the other hand, was raised in isolation in the mountains by his abusive, alcoholic father, who was also an assassin.
The Cracked article "5 Famous Historical Bad Guys (And Their Side of the Story)", which based on the url may have been called "How History's Bad Guys Got to Be That Way" previously. You can't put real life examples in "bad guy" tropes, but here it's the article saying they were bad guys, so whether you agree with it or not, it's clear the article is doing this trope.
The Koch brothers were raised by a literal Nazi nurse and a Social Darwinist father who made them fight each other.
Wayne Wheeler was a major force behind the Prohibition, inspired by being mildly injured by a drunk person when he was little.
Kaiser Wilhelm's crippled arm and terrible mother made him a total jerk.
George Wallace became a total racist after losing an election by not being racist.
Joseph Stalin basically declared war against all mankind after his girlfriend died.