Twisted Cogs has Joanna, who is regularly punishes the MC for talking to Ele, thinking he's imaginary.
Loads of Characters from the supervillain Web Serial NovelWorm, probably because in Worm people get superpowers due to being in really bad situations. The main character is the only member of her supervillain team, the Undersiders, who actually had caring parents.
The others were: Neglectful, drug-addled mother and a series of "stepfathers", none of whom were much better (Grue, Imp), Terrible foster care experience culminating in an over-controlling foster mother who tried to drown her child's pets (Bitch), Neglectful, overpressuring rich family that tried to exploit their daughter once she manifested powers (Tattletale), and a Charles Manson-esque supervillain who considered his non-powered kids wastes of space and his powered kids as prize jewels in his collection (Regent). And that's just the central team. A full list of every abusive parent or parental figure in the story would take up the entire page.
Aryan Nation, a white supremacist "superhero" from the Global Guardians PBEM Universe, admits that the reason he took to crimefighting was to repudiate the abuse his trailer-trash, redneck father heaped upon him while growing up, and is actually proud of the fact that he's not "some drunken Klansman in a bedsheet burning crosses", despite still being a racist Jerkass. The fact that he's doing the very same thing to his own kids that his father did to him hasn't occurred to Aryan Nation yet.
Fairly common as a backstory for characters in Survival of the Fittest, in that there are at least several examples per version. It was particularly common in v1 and v2, and while it isn't as common in later versions they still pop up. V2's Mariavel Varella is one such example, having been abused physically (and in a retconned thread, sexually) by her father, who also killed her brother.
Elsdon's father in The Eternal Dungeon series for no apparent reason at first and then in a strange, backfired attempt to "fix" Elsdon of his own sadism. Elsdon is understandably self-hating and mostly Ax-Crazy at the beginning of the series until he's given a chance to channel his own desires productively.
In Pony Dot Mov, Pinkie claims that her father forces her to shove glass up her vagina, but it's a bold-faced lie, made because Pinkie felt nobody was paying attention to her.
MSF High Forum: Destiny's mom wanted to possess her daughter to avoid growing old and dying, she killed destiny's father to do this followed by being killed herself along with Destiny.
In Touhou: a Glimmer of an Outside World, Marisa's father. Amongst other things, he threw her out—despite Marisa's being sixteen or seventeen at the most—and hit her when she tried to get back in.
In Nameless, it's heavily implied that Miller's mom molested him, which could possibly be the reason why he's so screwed up.
Generator's dad, in the Whateley Universe. Physically and emotionally abusive, especially after Generator's mother was killed (which may have been dad's fault). Generator would have been beaten to death if she hadn't manifested her mutant power right then. Money? All gone now that dad's on the run from the police for other crimes. The only reason dad didn't rape her is probably because she wasn't a girl back when she was living with her father.
Circuit Breaker as well - parental abuse doesn't get much worse than murdering your oldest child in front of the other two, then burying the body under a church pulpit and forcing everyone to pretend that the he never existed.
Ask That Guy and the Nostalgia Critic; Ask That Guy seems to think that he was never good enough and they told him that he would have go to back in the dumpster where they found him, while the Critic portrayed them as monsters ripping him apart in a kindergarten drawing. And Ask That Guy's response to "Why does Daddy hit Mommy?" and the Critic apparently hiding in the cupboard when he was scared seem pretty suspect, as are Critic's rants on dreams not coming true and parents putting pressure on their kids. Also, with Critic being a weepy Psychopathic Manchild and Ask That Guy having twisted views on sex and women, it was pretty obvious from the start.
Also treated for laughs was the The Nostalgia Chick's childhood. Her mother made her feel inadequate, her uncle sexually abused her and her father never gave her any love. Word Of Lindsay is that she retreated into always watching television to escape her parents yelling.
Played for Drama in Demo Reel, where Tacoma's family abuses him for sending his father to jail, Rebecca's parents make her feel worthless for not knowing what she wants to do with her life, and Donnie's family actually want him to be alone while they spend holidays with his wife.
The titular character's father in Dragomirs Diary is almost unreasoningly abusive and berating to his son, for no reason that Dragomir himself can muddle out. Oswald the Farmer is such a horrible dad that he essentially calls Dragomir a quitter after Dragomir is revealed to have died and been brought back to life.
Godzilla himself was portrayed as one in the earlier seasons of Monster Island Buddies, being quite neglectful toward Minilla and downright hateful toward Zilla. It's later revealed that the cause for this misbehavior was that his own father, the original 1954 Gojira, was rather rude toward him and outright consisedered him "the worst accident ever".However, after seeing Minilla scaring away Monster X/Keizer Ghidorah's army with a giant robot he built by himself, Godzilla has a change of heart and now aims to become a better parent. King Ghidorah is also shown to have issues with his own father, Monster X/Keizer Ghidorah, who in turn also has daddy issues with Grand King Ghidorah, his dad, who behaves pretty much like Abe Simpson with his son.
In Alfred's Playhouse, Alfred's parents were very neglectful of him, tried to drown him in the bathtub, and he is the result of an unsuccessful abortion. His abuse is the reason why he's so crazy.
''Random Assault": Mitch Rozetar was raised by Roman Catholics. Enough said.
All over the place in various GoAnimate videos, especially with the "Grounded" types.
RWBY: Weiss Schnee heavily implies that her father was abusive towards her and possibly her sister in an unknown fashion while they were growing up. He received a lot of stress from dealing with the White Fang's terrorist acts against the family's Dust Company, so he often would come home from work in a less than pleasant mood and lash out at his children.