In Masques, Aralorn meets a wolf (who is actually a man), and becomes his morality pet. While not exactly evil, he didn't care about most people beforehand having already done an heel-face turn by running away from his villainous father once he started to understand that human beings have feelings and torture is bad, and is fascinated by the fact that she doesn't fear him. She notices pretty early that he's not just a wolf, but still refuses to be scared. (She's a shapeshifter herself, so that's nothing that would creep her out).
Michael Grant's Gone series: Caine does this at the end of Hunger, either because Diana was bleeding out and she needed Lana to live, or because he realized how bad the Gaiaphage is.
Charles Dickens' Oliver Twist: Sympathetic heel Nancy, a prostitute who by default was a villain for her relationship with brutal criminal Bill Sykes, and at first enjoys her life. Nancy begins to turn after forming a relationship with the title character, a young street orphan who is kidnapped to be part of a band of pickpockets in London. Eventually, due to her desire to see Oliver become a respectable person, she decides to try to return Oliver to his family, but Bill brutally kills her before she can do more than give a few hints as to his location.
Ebenezer Scrooge becoming reformed by his experiences is the plot of A Christmas Carol
Hans Ebert in Chung Kuo, after having lost everything, does some serious soul searching and changes his ways.
Dolokhov in War and Peace goes from being a Manipulative Bastard of a Humphrey, something of a minor antagonist, to the trusted lieutenant of Vaska Denisov as the Russians chase the retreating French. He is still the same amoral asshole as usual (witness his reaction to the death of the little Rostov) - he is just putting is evil badassery to a good use.
In Fred Saberhagen's trilogy Empire of the East, Lord Chup served the evil Empire of the title faithfully ... until one of its warlords demanded: "You must be for once not brave, but cowardly.... It will be difficult only once. You must learn to cause pain, for the sake of nothing but causing pain. Only thus will you be bound to us entirely." Then he killed off a major demon, turning the tide of a critical battle. His Heel-Face Turn actually takes up the entire second book of the trilogy (The Black Mountains) and he goes on to become a major hero on the rebel side.
Harry Dresden refers this as the 'Vader Effect'. He is accused of it himself on several occasions, most notably when he joins the Wardens, the quasi-military magical police who have been on his back since his youth despite not actually changing sides. More specifically, the 'Vader Effect' is that feared enemies make great allies, because you know exactly how scary they are to the other guy. It's a natural extension of the expression "glad you're on our side".
As part of his backstory, Sanya, a large black Russian, in his youth took up a coin containing a Fallen Angel within, granting him power and what he presumed was the affections of the woman who drew him in. Upon learning she doesn't love him and sees him as a disposable pawn, he leaves and finds himself truly regretting his actions. This causes him to purge the demon from within and he drops the coin into a river. Soon after, a Knight of the Cross finds him and offers him a job, to join them and help bring more bad guys to their redemption. Sanya is know wielder of the Sword of Hope.
A far more dramatic instance is when Lasciel's shadow image, or Lash, is convinced by Harry that she has free will of her own and "dies" saving Harry's life.
In Changes it is revealed Martin, the most bland person is a spy for the Red Court of Vampires sent on a long run mission to destroy their enemy, the order of St. Giles. However, while there he saw the actions of his beloved king in a new light, and that the king truly is a monster that needs to be destroyed at any cost. He sets things up so well that by the end of the book, he gets Harry in a position to destroy all of the Red Court.
Angelina is the brilliant, beautiful, and psychopathic villainess of The Stainless Steel Rat. After she is captured and the psych-techs have worked on her, she marries the hero and becomes an agent of the Special Corp who doesn't enjoy killing. As much.
Mara Jade from the Star WarsExpanded Universe went from wanting to kill Luke to marrying him. That makes her Heel Face Turn queen.
A more minor example from the EU is Lara Notsil a.k.a. Gara Petothel of the X-Wing Series, who starts as The Mole. She ends up falling in love one of her "enemies" and growing affection for her squadron, causing her to turn on her Imperial commanders and greatly helping the Rebels defeat the Iron Fist.
Implied with the thief that was crucified next to Jesus according to the Gospel of Luke. He asked Jesus for forgiveness for his sins, and received it.
Acts of the Apostles: Saul who persecuted Christians until he had a vision from God and became one of the most influential Christians himself under the name of Paul the Apostle. Hence, in German, vom Saulus zum Paulus ("from Saul to Paul") is a common figure of speech for a Heel Face Turn, naming this very trope on the German language TV Tropes.
Downplayed in Montmorency. The titular character starts out as a liar, thief, almost a con-man, but by the end of the first book he's happily working for the British government, alongside Fox-Selwyn. However, he's still a thief with the alias of Scarper, he's just got better motives now.
In David Eddings's Malloreon, Zakath. Over the course of the third and fourth book of the series, he goes from being the brutal monster he is initially depicted as in the Belgariad, to a valued member of the group, and his friendship with Garion shows sign of bringing peace to the world finally. So long as they live long enough to do so.
Haven itself pulls one off in Manticore's eyes when, having just suffered a catastrophic sneak attack and with news a massive Solarian fleet is coming to attack the Manticore system, Haven President Eloise Pritchart shows up with intelligence revealing who has been responsible for many of the problems Manticore and Haven have faced, an offer not merely of a peace treaty (which was in the process of being negotiated) to finally end the war but one of a full military alliance, and a few hundred warships to help defend Manticore.
Inspector Javert in Les Misérables, whose world view explodes with the sudden realization that Jean Valjean is simultaneously a criminal and a good guy. To let Valjean go free would be unlawful, while arresting him would be immoral. Javert removes the problem by removing himself from the problem. He drowns himself in the river Seine.
There are quite a number of turns in the Harry Potter series:
The Malfoy family make a rather big one towards the end of the series; Narcissa makes the biggest change when she lies to Voldemort that Harry is dead so she can go into the castle and see if her son is alive. By doing this she saves the battle for the good guys. Her husband Lucius has quite a similar turn although he is not as active in his turn as Narcissa. Draco Malfoy's turn happens gradually in the sixth book when he is given a mission by Voldemort to kill Albus Dumbledore. At first he's extremely full of himself but as the year goes on, he buckles under the pressure when he realises that failure means his death. Dumbledore offers him a chance to officially make the turn and he begins to before he is interrupted. He makes another Face Heel turn in the final book but is reunited with his family. In the epilogue he and Harry appear to have abandoned their differences for good, although Word of God says that they are "not friends".
Regulus Black, Sirius Black's brother, joined the Death Eaters willingly but after Voldemort almost kills his house elf, Regulus realises what Voldemort is capable of and begins to have second thoughts. He finally dies in an attempt to steal and destroy one of Voldemort's Horcruxes
Kreacher pulls a mild one in Deathly Hallows after reciprocating all of Harry and Hermione's attempts at kindness with cruelty and hatred once he learns Harry is on the same quest Master Regulus was on, and died for, he warms up considerably. It also helps that Harry gave him the chance to hunt down Mundungus for stealing from "the most noble house of Black". He still never shows any remorse for his part in orchestrating Sirius' death or taunting him to the point of near Sanity Slippage while he was locked up in the same house in Order of the Phoenix.
Gellert Grindelwald has a small role but makes the turn anyway. As a child he had a friendship with Dumbledore but he eventually became an all powerful Dark Wizard until Dumbledore defeated him in a duel and he was imprisoned for the rest of his life. In the final book Voldemort attempts to get information from him about the whereabouts of the Elder Wand (he was the Wand's previous master) but he refuses to tell and is killed on the spot. Later Dumbledore remarks that some people said he felt remorse for what he had done.
To a lesser extent, so does Dumbledore himself. While in love with Grindelwald he enthusiastically accepts his pureblood supremacist views, and only rejects them when they fall out.
Dudley Dursley pulls one offscreen at the beginning of the fifth book after Harry saves him from some Dementors. Harry himself doesn't learn about the turn until the beginning of the final book. Word of God states they remain on Christmas card terms in their adulthood.
Garyl Shadowslayer from Shadowslayers pulled a heel-face turn at some point in his backstory, going from killing his mother and brother to risking his life to save the realm of Blackwood.
Wulfgar, in The Crystal Shard. The Reghedmen barbarians collectively attack the Ten Towns and are defeated by their militias led by Drizzt Do'Urden and Bruenor Battlehammer. Bruenor captures Wulfgar, barely more than a boy, and sets him to work in his forge. Ten years later, Wulfgar becomes the protagonist (of that book, at least).
Twigleg, in Dragon Rider. Working as a spy for the villain, he comes to genuinely like the hero and decides to switch sides.
Twice in The Stanley Family series. In The Famous Stanley Kidnapping Case, two of the kidnappers pull this and end up turning on their boss. In Janie's Private Eyes, former bully Pete Garvey, who is friends with the dog thieves, turns them into the police once he sees they're putting the Stanley family in danger.
Played with twice in Star Trek: Stargazer. In "Enigma", Obstructive Bureaucrat Admiral McAteer seems to defrost into a Jerk with a Heart of Gold. After a dangerous mission alongside Commander Gilaad ben Zoma, he appears to make a peace offering and reveal a more understanding side to his character. However, it transpires he was merely trying to manipulate ben Zoma. In Maker, murderous super-powered alien Brakmaktin also appears to be reconsidering his former conduct and having an epiphany. It turns out it was just him screwing with his captive.
In The Lion, the Witch, and the Wardrobe, Edmund Pevensie starts out as a self-centered brat who is easily manipulated to side with the White Witch against the Narnians and his own siblings. Later, when he is forced to see (and suffer) her cruelty, he takes the first opportunity to switch sides.
In Heather Tomlinson's The Swan Maiden, Doucette's sisters are cruel to her because she has no magic. When she discovers that she has magic, her sister Cecilia has one of these toward her, even though Doucette is now her rival.
This tends to happen in some Indonesian literature (Mostly KKPK, short for Kecil Kecil Punya Karya or 'Little Kids Who Creates') written by children. The thing that irritates is that in nearly every single one of the books that plays this trope straight, the rich, snobby Alpha Bitch (Always the Alpha Bitch, no exceptions) will turn good halfway through the story due to some event, and will instantly and melodramatically apologize to the hero, who instantly forgives her without any doubts whatsoever, despite the fact that they had been fighting since the first day of school. If not her, then it's her Girl Posse who will turn their backs at her because they haven't realized until today about how perfect, nice, religious, smart, etc the heroes are. Afterwards, the Alpha Bitches join the hero's group and have adventures like nothing has ever happened between them.
In Fusion Fire, Tel Tellai slowly turns from blind adherence to Phoena Angelo and aristocratic Netaian ideas about who is worthy to live to a genuinely Nice Guy who wants to work to reform the moral failings in the Netaian system.
Kthonia did this pre-series but seeing her daughter killed in front of her by a man leads to a Face–Heel Turn.
Becoming Benji's auntie mellowed Zarracka out. Not only does she help in the fight against Kthonia without a devious agenda but she volunteers to go back to her cell when it's over.
The Wheel of Time: Ingtar, Asmodean, and Verin, amongst others. Fans have debated whether Asmodean's Heel–Face Turn was genuine because Rand and Lanfear left him with little other choice, but Word of God has confirmed that it was. Verin may not count because she only swore an oath to the Black Ajah to escape death and study them from the inside, and appears to have intended to be The Mole from the beginning. Ingtar's example is played straight.
In The Host Wanderer's joining the side of the humans. She is not alone in this; other souls like Sunny and Burns do the same.
Aftran does this in the Animorphs series, although she's actually an interesting example; we never saw her as a villain, she was just very supportive of Visser Three and the Yeerk Empire.
In Worm, Bonesaw, considered one of the worst villains and a creator of terrifyingBody Horror, undergoes one, though she's not remotely trusted, and in constant danger of backsliding even though she does want to change.
As of the sequel it appears to have stuck.
In the Rainbow Magic series, a goblin in Sophia the Snow Swan Fairy's book does this, and Lydia does this in the movie.
In the sequel to Those That Wake, Arielle Kliest is fine wit torturing Mal and threatening him to get what the Old Man wants—but when she sees the totality of his plan, which involves assimilating every mind on earth, she's horrified and betrays him.
Ava Paige, who realizes the errors of her ways and the fact that no cure for the Flare virus will ever be found. She decides to become a Big Good and gets Thomas and the Immunes to head for the paradise she has prepared for them, free from the Flare virus.
A Mage's Power: After Duke Esrah's plot leads to Kasile being locked up in her own dungeon, Siron decides that enough is enough and frees her.
Origami Yoda: Harvey at the end of the 2nd book. He decides to stop antagonizing Dwight.
Wolf was a Lunar Special Operative tasked to find Scarlet so information could be gleaned from her about Princess Selene. However, he bonded with her on their trip to Paris while pretending to be helpful out of kindness. He changed sides for real when he saved her life before his brother tried to kill her. It helps that he never really like being a Special Operative, anyways.
Invoked in The Shepherds Crown when Tiffany decides to give the elf Nightshade (the former queen of the elves) a chance to learn about being human and helping others in hopes of bringing her around. It works... but she doesn't live long after proposing these ideas to the other elves.
Falk of The Dinosaur Lords, who's never publicly outed as a villain, gradually grows to respect his enemy and realizes that they're all in this together, eventually switching gears to be honestly on Jaume's side.
In the Malazan Book of the Fallen Karsa Orlong starts out as unambiguously villainous. Even at the end of his character arc he is far from entirely sympathetic, but arguably becomes either an Anti-Villain or a dark Anti-Hero. Some of this is arguably due to the narrative setting him against people who are unambiguously more villainous (Pedophile Priests, slavers, etc.), but some of it is due to Character Development, as his internal narrative makes it plain that he is re-examining the core beliefs that shaped him into the villain he was initially.
At the end of the Hellboy novel Emerald Hell, Brother Jester is given back his humanity via the piece of his shadow that was cut off and Hellboy says to him "Go and try to sin no more", keeping with the Christian themes present through out the story (as it takes place in the Deep South around Enigma, Georgia). Brother Jester then leaves and tries to make good on both his promise and the good guys' mercy.
Attorney Arcinas in Smaller & Smaller Circles, who goes from stonewalling the priests to helping them after he screws up badly by arresting an innocent man for the Payatas murders and indirectly allowing another murder to occur.
This is the main plotline of The Bad Guys series. The four main characters decide they're sick of being the bad guys (Mr. Wolf in earnest, the other three through convincing), and decide to become good. Unfortunately for them, they're not the best at it.