Francis Dolarhyde from Red Dragon. Sure, he murders whole families and rapes their corpses, but good lord, he had an awful childhood. It gets to the point where you want him to be caught, but you still kinda hope he gets out of the whole mess all right. It helps that Dolarhyde's character development throughout the novel is basically him Fighting from the Inside to prevent a Split Personality Takeover, motivated by The Power of Love. That's enough to make anyone sympathetic.
JameGumb is implied to be one. Hannibal himself states "Buffalo Bill wasn't born a criminal; he was made one by years of systematic abuse]]."
Hannibal himself is definitely one. His idyllic life was shattered when his parents were murdered and he and his little sister were abducted by German deserters who ate his sister and fed him some of her in a broth. No wonder he's Axe Crazy.
The title character from the Balzac classic Cousin Bette could easily been seen as a female analogue to Heathcliff: childhood abuse, poverty and abandonment by the one man she ever loved (who probably never returned her feelings to begin with) drove her to a monomaniacal obsession with revenge, from which no-one in her path is safe.
Ineluki the Storm King, the Big Bad of Tad Williams' Memory, Sorrow, and Thorn. It is said that he was the brightest light the Sithi had ever known and, had things been different, he might have led them out of their exile and into a new golden age. Instead, he went down dark paths, sacrificing his family, his soul, and ultimately, his life to defend his people against the depredations of humanity. Even after death, his hatred sustained him, turning him into a dark spirit that seeks now to return everything to Unbeing in revenge for his suffering. In the end, this turns out to be the key to his defeat.
Frankenstein's Monster (in the original novel, that is). All of his rage against man, and against Victor Frankenstein in particular, would be gone if just one person bothered to look past his macabre appearance and associate with him. But Humans Are Bastards, so... The 1994 movie based on the novel did manage to get that part right, with the motivations of the monster laid bare.
Gollum in The Lord of the Rings. After centuries of misery and torment, he nearly destroys the quest (dooming Middle Earth to tyranny) because of a Heel Face Door Slam. Ironically, Frodoknowingly claims the ring after suffering months of psychological torment because of it. Fortunately, the quest would have failed without his attempt to prevent it. Bilbo, Frodo, and Sam taking pity on Gollum was necessary for the Ring's destruction; and expressly choosing not to attack and kill him on four separate occasions, even on the slopes of Mount Doom...
Frodo: But do you remember Gandalf's words: "Even Gollum may have something yet to do?" But for him, Sam, I could not have destroyed the Ring. The Quest would have been in vain, even at the bitter end. So let us forgive him! For the Quest is achieved and now all is over. I am glad you are here with me. Here at the end of all things, Sam.
Galadan Wolflord from The Fionavar Tapestry turned rather genocidal towards mortals after one stole his girlfriend - but when said mortal wound up getting her killed, he went crazy and decided that the only way to end his pain was to destroy the universe. The only time in the trilogy he shows genuine emotion is when he finds some of the heroes apparently "desecrating" his shrine to her, and at the very end, when the heroes spare him and he realizes that there is some good in the world - and in himself.
Dragonlance: Raistlin Majere has a life that progressively increases in Suck, until he decides that he's going to take vengeance by becoming a GOD. And he does it, too. After he finds out that his godhood will destroy all of creation, leaving only himself in an empty universe, he...does exactly the same thing.
More specifically, that was an alternate-future Raistlin who was insane at that point. When main-timeline Raistlin realizes the consequences of his actions, he does repent and sacrifices himself to save both the world and (to him, more importantly) his own soul.
In Malazan Book of the Fallen by Steven Erikson, the Crippled God is in constant pain after being forcibly summoned and having subsequently crashed into the planet like a meteor. The Crippled God now tries to share his pain with everyone else. Several characters have speculated on whether or not his followers' twisted faith won't let him heal or is it that his pain twists the followers' minds (even more). He's also poisoning the goddess of the Earth, pushing him into full on Omnicidal Maniac territory, as he spreads chaos and death across the known world.
In Alan Dean Foster's Humanx Commonwealth series, Flinx's "sister" Mahnahmi is given this treatment in a big way. Considering how messed up she is and what she's suffered in her life, it's hardly surprising that she's become nihilistic, but for some reason, she insists on taking Flinx and everything he loves with her, even while he's busy saving the galaxy.
The Lazar from The Death Gate Cycle have this as their hat - they are undead beings caught forever in a state of hellish agony between life and death, and the only way they can have any release at all is by delivering others into the same torment. The only real exceptions are Jonathon (who's a straight Woobie mixed with Messianic Archetype) and, ironically, Kleitus, leader of most of the Lazar. He was enough of a Magnificent Bastard in life to keep his head following reanimation (though, admittedly, he's a bit more Ax-Crazy now), and plans to use the other Lazar as his tools to purge the universe of sentient life, so he'll be left ruling an empire of the dead.
The Chandrian, specifically Lanre, in The Name of the Wind; Lanre went insane when his love died, and, in the unsuccessful attempt to bring her back, made himself immortal. With suicide now not an option, he decided to kill the rest of the world instead. He's definitely sympathetic in the Back Story, the only question is if he can maintain it as Haliax in the modern era.
While most of the villains in Sword of Truth are Omnicidal Maniacs, Nicci is more of this trope. The sixth book, Faith of the Fallen, is mostly devoted to showcasing her mindset and point of view.
Inverted (and literal) in Death Star with Tenn Graneet, the station's chief gunner. Rather than someone who commits evil acts because of his painful past, he is a somewhat naive Just Following Orders commander who believed that the Empire would never fire the Death Star at full power at an inhabited planet. When he realizes that they would and he carried out that order, he becomes so full of self-loathing that you start to really pity him. Eventually, during the Rebel attack at Yavin, he stalls for a few critical seconds, allowing Luke to blow up the Death Star before the Death Star could blow up Yavin IV.
Qwi Xux, one of the chief engineers for the Death Star's superlasers, and the creator of the Sun Crusher: she was taken from her village as a little girl and placed in a high-risks and genuinely horrific mathematics/science course with other students, where their lives depended on whether they got the answers right or wrong, and those of their village (if one of the students gets even one answer wrong, the student in question will be forced to watch as their home village is blown away via aerial bombardment and executed shortly thereafter). She was the sole graduate, and the sole survivor of that course, which was also headed by Imperial Grand Moff Wilhuff Tarkin, and it was because of this that she felt driven, to the extent of borderline psychotic obsession, to solve any problem whenever the Empire declares that it wants a solution, often feeling not responsible if it turned out to be a failure in faux-naivete.
There's also the Grand Admiral Osvald Teshik. Because of a failure in regards to rescuing Coh Veshiv from the Rebel privateer Far Orbit, or any reason to begin with, as he implies that Palpatine did this to him for absolutely no reason whatsoever, he ends up being nearly killed in a battle that Palpatine ensured that he would not win, and that he turned into a cyborg with 3/4s of his body removed, and the near-death experience, and the abuse by various Imperial personnel for his cyborg status, left him extremely cold and nihilistic up until he was saved by a construction worker, and he ends up explaining the battle to the Rebels and the impact it had when he is to be executed for war crimes, having been resigned to his fate, before emitting a mechanical, almost pitiful laugh upon his death.
Isabella Sordeno from Mindy Mackay's Peacebreakers seems to fit the bill. After being manipulated, abused, and operated on while conscious, she snaps and loses her mind, developing into a strategic mastermind and almost singlehandedly conquers a country while exploiting and manipulating everyone around her For the Evulz. Eventually, as her malevolence snowballs, her reckless strike against an old enemy ends up breaking the world.
Trashcan Man in The Stand plays a role quite similar to Gollum in The Lord of the Rings, which makes sense, seeing how the latter was a big inspiration for the former. He actually destroys the entire Evil Realm of Las Vegas, turning nearby states into radiation zones to prove his loyalty to Flagg by bringing him the Big Fire to destroy the people of Boulder. This only occurs because Flagg promised him protection from the voices in his head of the people in his hometown who used to tease him for his insanity and pyromania. When one of Flagg's minions use the same language to insult Trash, he snaps and blows up an airfield, and flees into the desert with a price on his head.
Funny thing, the other guy wasn't even insulting him, he was only making a rude joke of sorts and involuntarily triggered his Berserk Button.
Luke from Percy Jackson and the Olympians to the point when even the victims of his nefarious acts (Silena, Thalia, Annabeth) show compassion for him and want to help him. Even Percy, who out right resents him feels bad for the guy in the end.
Dear god, Aeglyss, the halfbreed from The Godless World Trilogy. After a lifetime of ostracisation and failed attempts at social interaction, he's so damaged that his very presence is contaminating the planet and poisoning the Shared. By the end, he's diseased, physically ruined, and ready to die, and tries to take the world that's rejected him along for the ride. It's not even deliberate: after failing to enslave the world, he just doesn't care enough about it to try and stop the destruction he's begun.
Carrie from the book of the same name by Stephen King. She was the Butt Monkey for her entire school life, and at home, her mother beat her, verbally abused her, and locked her in a small closet for up to a day at a time. And she weathered all of it. When she found out that she had telekinetic powers, she exercised them to make them stronger, but not to get revenge. She never even contemplates revenge. But finally, one last, cruel prank goes too far, and the poor girl snaps, taking out of all of her pain and misery on the town around her.
Q Squared, the Star Trek Novel by Peter David, features Jack Crusher in an alternate reality, a good but unhappy man who is targeted by the godlike Trelane, who drives Jack murderously...and suicidally...insane
Persephone in Ravirn releases the Necessity virus that would have destroyed the entire multiverse without Ravirn's intervention in hopes of breaking Hades' hold on her. It's later implied that she would have done the same again when Hades is one of the few candidates to replace Necessity and gain absolute power, except that she trusted Ravirn to stop him instead.
The Bane (real name Pearlpelt) from The Underland Chronicles. His father killed his other children so Pearlpelt could have more milk and grow stronger. His parents killed each other in a fight, and he saw his mother lying dead with her innards spilled over the ground. To make matters worse, almost all the humans shun him because he's the Bane, and many of his fellow rats honor him and want him to be their king. Eventually, he goes completely off the deep end, becoming an Evil Albino and a great Hitler allegory.
Ari from the Maximum Ride books. He was born a sweet, innocent child, but he grew up in the shadow of his half-sister, Max. He was turned into a Wolf Man by scientists, and was subject to constant genetic enhancements afterward, eventually becoming a hideous freak. In the end, though, he gets a Heel-Face Turn—but too late.
Ghwerig the troll from The Elenium. In reality, he is maddened by the loss of Bhelliom and devotes most of the rest of his life to searching for it, and though he eventually finds it, he is killed by Sparhawk and Kurik.
Doesn't seem like it at first, but Petyr Baelish from A Song of Ice and Fire. He was born as one of the poorest nobles, if not the poorest noble, in the realm, then separated from his family at a young age to live with another family in much, much better standing—throwing in his face what he will never have. He's small, weak, and looked down on by everybody. Nobody even calls him by his real name. Then, just to make things worse, he falls in love with one of the daughters, who he isn't allowed to marry because of his birth. He nearly gets himself killed fighting for her and, after he loses, she completely ignores him. Hard not to feel sorry for him...until he becomes a puppeteer in the royal court, ruins his first love's family and kidnaps her teenage daughter, kills people off at his convenience, and starts a frickin' civil war.
Catelyn Tully, who turns into a homicidal, undead, noose-happy outlaw leader after witnessing the brutal massacre of her son, herself and companions at a wedding feast, having already lost her husband and her other four children.
Barty Crouch Jr.. He's a "Well Done, Son!" Guy with a father who never cared about him whatsoever, who loved his wife and work far, far more than his own son. He's also incredibly brilliant, one of the few characters to get twelve Outstanding OWLs in the series (not even Hermione got twelve Outstandings), probably got all Outstandings on his NEWTs, too, possibly just to please his father. After failing to receive the love and approval of his father, he joined the very faction his father despised, finding approval and a father-figure in Voldemort. Crouch was then sent to prison with little consideration by his father, who proclaimed that he had no son. He's well aware that his father saved him from Azkaban and eternal Mind Rape via Dementors because his mother begged him to save their son. She herself was dying. The only parent who loved him gave up her life for him and died, and by this point, Crouch was already halfway to madness. It's strongly implied that being under the Imperius Curse for too long has the same effect as Mind Rape, and he was under one for thirteen solid years thanks to his own unloving father. It's no wonder he stayed very loyal to Voldemort and helped with his ploy to get Harry killed and killed his own father.
The eponymous character of Skulduggery Pleasant was this after his family was killed. The books always implied that he went a bit off the rails, but in Death Bringer, we find out that it went a tad further than just Unstoppable Rage. He's Lord Vile.
The novelization for Disney's Snow White and the Seven Dwarfs paints Queen Grimhilde as an extremely dark Woobie, Destroyer of Worlds. For starters, the novel gives her the Freudian Excuse that she was emotionally abused by her father, a mirror maker, who refused to acknowledge that she was beautiful since she was a child, leading her to be insecure in regards to her beauty. When she did marry Snow White's father, the king, she actually did genuinely care for Snow White as if she were her own daughter. Unfortunately, her father's witch cousins ended up giving her a gift (the magic mirror) that also housed her father's spirit, and it is heavily implied that it was thanks to her father's haunting influence that she started to go insane by the movie.
Elric of Melniboné just can't get a break. Every time he kills it makes him stronger and it also makes him hate himself more. On top of that every girl he loves (each of whom wants to wrap him in the proverbial blanket and feed him the proverbial soup) dies, which usually leads to him needing to wreak revenge on someone. And kill them with his sword and take their soul, and then hate himself. It's a vicious woobie cycle.
In Death series: Holiday In Death and Portrait In Death have killers who could be considered this. Those killers suffered losses that was the end of the world for them. They turned to murder because for them, it's the only way to unleash the pain. Those killers are also implied to have been born with untreated mental disorders. Perhaps they are unsympathetic, but it can be agreed that they are pathetic.
Most of the characters who play in "Battle Royale", particularly Yuko.
Brittney Donegal from the GONE series plays a prominent role in the attempts to wipe out the entire population of Perdido Beach with giant man-eating bugs (PLAGUE). But even though she's persists in helping the ongoing genocide attempts by her master, even Sam the hero and big good is reluctant to try and stop her, actually apoligising for ruining her evil plans.
Brittney has been enslaved, tortured numerous times in horrific ways, disfigured, has her only family killed and spends three months in a grave in the duration of the series. She's only in four books and Isn't even a significant character in two of them. Can you really hate her in spite of the genocide attempts and destruction she caused?
In A Kiss in Time, it turns out that the evil witch who cursed Talia and wants to kill her actually used to be a kindly fairy who helped the royal family. She'd been in charge of watching Talia's older brother (then an infant) while he slept, and noticed too late that he suddenly stopped breathing. She tried unsuccessfully to revive the baby using her magic, only for the child's nanny to walk in and declare that she cursed the boy to die. She was then exiled and reviled as an evil witch.
Exploited in Robert Jordan's Wheel of Time. It is revealed in the twelfth book that the Dark One's plan is to force Rand al'Thor to become this. It nearly succeeds, until Rand is saved by the mad voices in his head.