Lord Tedd may or may not have one. Consider the facts that he is the most powerful known being in the comic and that the creator admitted that people wouldn't like his backstory because it is just that sad. The adults in the prime universe (which is a decade or so behind Lord Tedd's) seem to believe he has one though, and are going to a lot of effort to make sure their Tedd doesn't suffer the same fate. For example, Raven is reluctantly willing to take Grace on a hunt for a dangerous boar...until he finds out she's Tedd's girlfriend, at which point he freaks out, and only agrees to take her under extreme duress.
Raven: You will follow my orders without question. If there is danger, you will leave me to die. Do I make myself clear? Grace: But— Raven:Do I make myself clear?
Susan also had a couple of events that shaped how she was now. The event that shaped her Straw Feminist views on men was she catching her father with a naked women who was not her mother, and her mother being a Straw Feminist herself, this is also the reason why she dyes her hair dark-blue. She also used to be a literal Wide-Eyed Idealist before her trip to France where she and Nanase were hunted by a vampire-like Abberation, and Susan being forced to kill it. Thankfully after a couple of arcs, she has gotten some closure and a less strained attitude.
In Fans!, Alisin Oberf, during her dark days when she was dying of a rare disease, was, beneath her Perky Gothexterior, a self-loathing mess, who took pleasure in heavy bondage and sadism. Years later, after she was cured of the disease, but not her negative self-image, one of her "partners", Keith Feddyg, emerged as Alisin's greatest nemesis, using her own self-loathing to force her to become his sex slave and blaming her for his having become a psycho. Subsequent evidence indicates that he was alreadythere before Aly ever showed up.
Also, Alisin killed Robert's goldfish, which may or may not have something to do with the latter's eventual world dominating ambitions.
Joel Calley from Concession has about three Freudian Excuses: his father left their company to his older brother Julian, his sister Miranda was killed by Julian when they were young, and their parents blamed Joel for the murder and put him in an asylum where he was sexually abused by a doctor. There have also been a couple of throwaway gags which, if taken too seriously, could imply that his mother resents him for not being a girl. If there was a trope for Freudian Sue, Joel would probably be the poster boy. However, much of, if not all of this is ultimately subverted when it's later revealed that Miranda actually died in her sleep and that demonic Miranda encouraged Joel to do bad things so she could feed on their suffering. It must be noted Joel willingly helped her and was already sadistic. When confronted about this, Joel immediately notes that his and Miranda's real motives are to gain power. In the end, Joel's only real excuse for his actions is that he's a goddamn psychopath.
Token Evil Teammate Belkar spins a sob story about being mocked as a child and becoming an adventurer to get strong enough to take revenge. However, he only says this to get free experience points for proper role-playing.
Played straight with Redcloak, who lost his village to the crusading of the Sapphire Guard as a child.
Might also count for Nale, Elan's evil twin and The Unfavorite to their father, General Tarquin. He's evil, but incompetent because of ego. What he wants nothing more is to be his own man, and step out of his father's shadow and manipulation. Tarquin agrees to this, since it was the only thing stopping him from avenging Malack.
Pops up twice in Kevin & Kell: Ralph constantly tried to hunt and eat his brother-in-law Kevin because he didn't want his sister to go through the same heartbreak he did when his herbivore lover died in childbirth. More recently, Desdemona Fuscus tried to push Lindesfarne and Fenton to marry earlier and earlier. This was because she was secretly a vampire bat, and didn't want Lindesfarne to find out and call off the wedding.
Flik's whole motivation. Since we see the problem before we see its results, it's rather differently played than normal.
Ménage à 3: The characters from this comic mentioned below aren't actual paid-up villains, but they still have excuses.
Gary's virginity and sexual dysfunction are allegedly a result of his severely repressive ultra-religious parents, plus cockteasing girls in his teen years. (And he lives with two women who engage in a lot of sexual teasing, albeit mostly by accident, and lusts after a girl with penis-phobia. Um...) However, this has never been mentioned again since the early strips in which Gary told the story, and the writers may not consider it very important; Gary's problems don't need that much explanation — he's just a hopeless geek, with his geekiness turned up to eleven. And when his mother 'phones to wish him a happy birthday, she sounds nice enough.
The root causes of Kiley's runaway A-Cup Angst are apparently finally revealed in strip #916 (August 07, 2014, NSFW). They go back to her teenage years.
Off-White: She's not a villain, but the tragic death of most of her litter is at least partly to blame for Jera's attitude.
Vriska from Homestuck is partially a HUGE BITCH BLUH BLUH because her guardian was a giant spider to whom she had to regularly feed other young trolls or be eaten herself.
Drowtales: Ariel, the 'main character' of the story. The first 10 years of life were dominated by an sociopathic stepmother who envied her own child. And then forced by her high-standards grandmother to murder some punk who tried to kill her. And finally realizing that living up to her grandmother's standards caused her to fail in protecting her best friend. By the time she's done with all that, she lashes out at one of her friends and ends up killing an innocent in the crossfire. Once this happens she has a My God, What Have I Done? realization and moves off the Villain Protagonist path to a more heroic one.
Also claimed by Snadhya'rune, who is effectively the Big Bad, who says that the pressure her mother the Empress put on her and the death/posession of her "twin" Khaless made her crack and eventually murder her own mother. It's suggested in story this is bullshit and she's actually a straight up sociopath, though.
Snadhya's daughter Kalki, on the other hand, may have a genuine one since her mother passed her off to servants and never showed her affection, making Kalki a desperate Attention Whore who feared she would be replaced, fears that were founded when Snadhya killed her in cold blood saying she was nothing but a tool.
Jamie from Khaos Komix is a foul-mouthed homophobe who bullies Alex for supposedly being gay and disowns his best friends after they come out to him as a gay couple. Then you learn that he was sexually abused as a child and has a mother who doused him in scalding water when she caught him Playing Doctor with another boy which has led to him having massive issues about sex and sexuality and you wonder why he isn't even more messed up. However, he actually criticizes the use of this trope by stating that he doesn't believe that his traumatic past excuses his actions and that he still has to work hard to redeem himself.
In Freefall, Edge spent his formative years in a warehouse surrounded by unintelligent machinery. Robots using Dr. Bowman's A.I. architecture, like humans, need proper socialization, and he's turned out with an It's All About Me attitude and the complete conviction that he's always the smartest (and most important) person about.
Sticky Dilly Buns has Ruby, who was traumatized at the age of about 14 when she discovered that her sister Amber was a porn actress - by being exposed to one of Amber's videos at a teenage party. Okay, that involved her sister rather than her parents - but the problem seems to have been compounded by having to keep Amber's secret from their parents for the next several years. Fortunately, her "villainy" is limited to a fear of men and a petulant attitude towards Amber, but it makes her hard for Amber to live with.
The Bedfellows strip where Sheen starts seeing a shrink reveals that his bad attitude can be traced back to when he was heckled out of a kindergarten play. The hecklers? His parents!