The Psycho for Hire Akabane of Get Backers (AKA "Doctor Jackal") used to be an actual doctor who saved people, but failed to save the son of a good friend. That is the origin of his current personality.
In Weiss Kreuz, Schwarz's resident Ax-CrazyKnife Nut Farfarello started out as a devout Catholic child, but when he learned that he was adopted and that the nun who was his teacher was his biological mother, he had a psychotic episode and murdered his entire adopted family. As an adult he claims that his desire is to kill God, and spends his spare time torturing priests to death.
In the Soul Eater manga, Justin Law pulls an ultimate Faith Heel Turn and kills BJ because of imposed insanity from The Clown. The thing is he doesn't lose his faith. He instead comes to view religion as a form of insanity and therefore converts to the god of insanity.
Rurouni Kenshin's Yukyuzan Anji is a particularly heartbreaking example, though he's not an awful person by any means. He turns from an extremely kind, devout, and physically unimposing Buddhist priest to the hulking fallen priest that he is in the Kyoto arc when the children under his care are trapped inside his temple and burned alive, due to the village head hoping to curry favor with the new government and its emperor-centered Shinto.
Even worse, this is based on actual history, as the Meiji cut off government sponsorship of temples to promote their new standardized form of the "native religion." (The orphans are kinda a stretch, though.)
This is the premise of the motivation for the Joker Captain Ersatz, Mr. Rictus, in Wanted, a kindly and religious man who was horribly scarred in a fire and, while on the operating table, died but found no afterlife.
The minor Marvel Universe villain Madcap went there first, save that he also got total immortality and superpowers in the same accident that killed his entire family and church group, making for even greater nihilistic nutsiness (though not nearly as much evil).
The main character from the title story of Will Eisner's A Contract With God is like this. Having lived his life as a good Jew only to lose his adopted daughter turns him into a slum lord.
Being Will Eisner, though, he makes it both convincing and tragic.
At least one Chick Tract does this, possibly a few more. Act surprised.
The most perplexing (and unintentionally hilarious) example would have to be the one where a child grows up to become evil...because he found out there was no Santa Claus.
A lot of FSTDT quotes feature people who fear having a crisis of faith because they believe this will happen.
The book Supervillains and Philosophy has an essay speculating about Two-Face's philosophical journey. (Obviously, this is a completely non-canon Alternative Character Interpretation.) According to this essay, Harvey Dent aka Two Face was a believer in the strongly ordered universe of Calvinism when he was a young man. But when he went to college and learned about atheistic philosophies like Existentialism, he began to believe that his two-faced random destruction was more appropriate to the true nature of this chaotic world.
In the 1993 DC ComicsBloodlines crossover, a priest was attacked by one of the alien parasites. He awoke afterwards with a crisis of faith and decay powers, leading to him embracing evil and calling himself Cardinal Sin.
Likewise, the man who held a shotgun on the priest was attacked and discovered he now had healing abilities and actually saved the priest before he died, now calling himself Samaritan. Samaritan ended up dying as he managed to cancel out Cardinal Sin's death touch.
In Bram Stokers Dracula, Dracula is originally a very pious nobleman, until one day, while he is busy fighting off the enemies of the Church, his wife is tricked into thinking he's been killed in battle, so she commits suicide out of despair. The priest tells him that, sorry, suicides are damned for all eternity, nothing to be done about it. Dracula does not take this news at all well, becoming his Start of Darkness.
Salieri in Amadeus does this after continually being upstaged by the boorish, spoiled, conceited, but vastly more talented Mozart, ultimately deciding to steal his work and drive him to his death, because he couldn't stand that God had made Mozart more gifted than he. Inverted in that even beforehand he was really a Jerk Ass whose faith in God was basically an extension of his personal vanity.
The Gone series: Britney in Plague. Also Astrid, after seriously questioning her faith, becomes much more of an Anti-Hero.
The Sparrow: Emilio Sandoz seems to have this at the beginning of the novel. Much of the book is finding out what exactly happened.
An inversion, but not a Heel-Faith Turn, occurs in Elantris with Hrathen, whose growing doubts over his religious faith cause him to turn against the Big Bad. From the villain's perspective, this would be a straight example.
Robert Putney Drake, in Robert Shea and Robert Anton Wilson's Illuminatus! trilogy. Born a Boston Brahmin and destined for greatness, he serves in the American Army in WW 1 and is changed forever by being the last man left alive from his platoon. Returning to the USA, he starts small by heckling street preachers. A combination of survivor guilt and a conviction there is nothing turn him into a ruthless monster.
The Wheel of Time series has a justified example-general hedonist and Manipulative Bitch Graendal was once one of the most faithful and diligent asthetics in the world before her fall...except she was also a complete Control Freak and egomaniac, who did her turn when she realized she couldn't force the world to be like her. Her new persona is basically a spiteful commentary on her disgust for the world. Justified, of course, in that she fell from grace primarily because of her pride and inability to admit the world had problems she couldn't fix. Losing her faith was just a manifestation of it.
In his case it was an unfortunate case of In the Blood, though.
Averted (or perhaps inverted) with Father Dougal of Father Ted. While Dougal often makes comments which would perfectly fit this kind of character (e.g. something like "Todd, we're not really supposed to believe in that Jesus stuff, are we?"), he is The Ditz and presented as a better person than the more faithful Ted.
Star Trek: Deep Space Nine has a bit more gradual version: Kai Winn was always jealous of Sisko for being the one the Prophets chose as their Emissary, and the fact that they didn't communicate with her wore on her more and more. Then the Prophets' Evil Counterparts, the Pah Wraiths, do show her some attention, and by this point, that's enough to drive her over the edge to real villainy as their servant, working alongside Gul Dukat.
An example where the person doesn't turn evil, but still gives up on life, occurs in the Star Trek: Voyager episode "Mortal Coil", where Neelix dies and is brought back to life. He has no memory of experiencing the Talaxian idea of the afterlife (where you go to a forest in which you're reunited with dead loved ones). Because he lost his whole family in a war, that belief was the only thing keeping him going, and it takes Chakotay to talk him out of suicide.
Ryan Hunter from Joan of Arcadia apparently suffered one of these (of the Smite Me, O Mighty Smiter variety) prior to his first appearance, leading to his becoming a church vandalizing, puppy-kicking anti-theist. Had the show survived for a third season, Ryan would've been Joan's Evil Counterpart.
An early episode of Stargate SG-1 had a religious guy go crazy and take over another planet with intense UV radiation as its god. What's particularly ridiculous about this is that no less than two of his teammates joined him. The one that didn't showed up in later episodes a few times, while the rest all died. Someone really fucked up the selection process for that team.
Used along with Heel-Faith Turn in My Name Is Earl. A Scary Black Man gangster who went by "Hash Brown" and eventually became a priest ends up being on Earl's list at least five times, with each new list item revealed making him angrier and angrier until he snaps and decides to return to his gangster life. Then Earl recognizes his car and reveals that he broke the taillight on it (another list item). The broken taillight caused Hash Brown to get pulled over and be late for a deal which ended up turning into a brutal shootout, meaning that Earl had indirectly saved his life. Since this event was what had caused him to take up religion in the first place (he originally attributed it to divine intervention), he thanks Earl and goes back to being a priest.
In the Doctor Who episode "The Unicorn and the Wasp", the Reverend's homicidal madness came along with a prideful scorn for the faith he'd followed all his life.
Older Than Feudalism: The Book of Job subverts this trope. Satan posits that Job is only a good, religious man because he is prosperous, and that if he suffered, would curse God. Satan attempts to test this theory—messengers arrive informing him that all of his livestock were stolen or killed, as well as his servants and children. When that isn't enough, Satan afflicts Job with illness. Job refuses to curse God, despite urging to do so by his wife and his friends—though he does finally break down and ask God "why?" God sharply rebukes Job and his friends, but rewards him for his faith by doubling his family and possessions.
Exalted has an unusually sympathetic example in the form of the Blood Queen, who used to be one of the Brides of Ahlat, an Amazon Brigade symbolically and literally Married To A God. The Brides of Ahlat are not permitted to sleep with any other man, on pain of death; a little-known fact is that this extends to rape. When the woman who would become the Blood Queen found this out the hard way, she renounced Ahlat, fled Harborhead, and became an akuma in order to take revenge on the entire institution that had ruined her life.
This is a big part of the presentation of Salieri in the play Amadeus. Salieri starts out, as he tells the audience, a pious man living a staid life. His beliefs are called into question when he meets Mozart and doesn't understand why a borderline Jerk Ass like Mozart gets divine musical talent but he doesn't. Thus, Salieri renounces God, and actually experiences improvement in his status from that point onward.
Neverwinter Nights features paladin Aribeth de Tylmarande, who turns from Tyr, God of Justice, after her lover Fenthick Moss is unjustly executed for being an Unwitting Pawn. She then goes on to become commander of the BigBad's army. You can choose to try and redeem her towards the end of the game.
Grandia II has Pope Zera, who discovers that God is (literally) dead and sets a plan into motion to resurrect the world's equivalent of Satan so he can destroy the world.
Vandal Hearts II has Yuri, who was intensely religious throughout all of his childhood and most of his adulthood, until learning about the deception behind the game's major religion. It wasn't enough to turn him into a coldly calculating supervillain from then on or anything, but it did lead to a Heroic BSOD and eventually made him Ax-Crazy just long enough to attack the party. Whether you kill him or successfully talk him down depends on whether you have 100% Completion on the game's hidden plot-relevant treasures and such.
In the Assassin's Creed series, this is pretty much how the Templars fall after learning that all miracles and works of God were actually the result of powerful ancient technology.
In Xenoblade, the goddess Meyneth is a kind and loving deity who just wants to protect life on the two titans even to the point of pulling a Heroic Sacrifice to do so. However, because of her desire for peace between the two worlds, her most loyal supporter - Egil - turns on her; believing that his people must take revenge against the Bionis.
Related to the Dracula example above, Castlevania's Dracula also renounces God after his wife died while he was busy fighting the crusades.
Diablo III has Jondar, a former knight who turned necromancer when he discovered the corruption within his holy order. Kormac, in his quest to figure out what it was Jondar discovered, asks the player character to kill him if he shows any signs of turning bad like Jondar did.
Subverted in Homestuck: The complete and utter deconstruction of his religion was one of the several factors resulting in Gamzee Makara's insanity-induced killing spree, but he goes back to his faith afterwards and remains every bit as evil.
In the two-part episode "Lost in Parking Space", the devoutly religious Princess Clara is led to believe that the Rapture has come and taken her friends but left her behind on Earth. After she signs her soul away to a man she believes is Satan, she decides that she enjoys being evil and promptly goes on a rampage. When she discovers that the Rapture didn't actually come (her friends just ditched her to go to the mall), she changes back.
Bob the Cucumber in "Clum Babies" goes on a murderous rampage and kills the entire cast when he is told that the Bible is open to interpretation.
Played with on The Simpsons when Ned Flanders loses faith after his wife dies, turning the picture of God away from him and scaring his kids with his decision not to go to church.
Ned: No, I'm not kidding. I'm going to sit right here and miss church. You just watch. (Smash Cut to Ned driving his car and looking Heavenward) Sorry, sorry, sorry, sorry, sorry!
It's more a parody on the Book of Job than Ned fully losing his faith.
Lampshaded in "Lemon of Troy" when Bart is handing out roles to the members of his team. He designates Todd Flanders "the quiet religious guy who ends up going crazy".
In American Dad!, one episode has the rapture happen. Stan is completely bewildered that he had been left behind and tries desperately to get into Heaven, including trying to convince (fake) Jesus Christ that he is more worthy to be sent to Heaven than his wife, Francine. Francine is naturally ticked off by Stan's behavior and she abandons him, but she runs into the real Jesus and she rubs it in to Stan before she is whisked away by Jesus. Cut to 7 years later when the war between Heaven and Hell breaks out on Earth where Stan is now a hardened and scarred hunter who has denounced Jesus and God because despite doing what he thinks was being a good Christian, he was still left behind. Stan's faith is slowly restored though once he learns from Jesus that Francine was captured by the Anti-Christ and he vows to save her after Jesus promises Stan entry to Heaven.