A milder but still very impressive example in the same book occurs when Narcissa Malfoy lies to Voldemort about Harry's death, thus protecting him, as her only remaining motivation is her love for Draco. It eventually leads to the Malfoy family being pardoned for their crimes.
This is the defining trope of Harry Potter. If a character truly loves another, then they become at least somewhat sympathetic. Inversely, all of the characters who don't love are pure evil. There are very few exceptions to this rule in the series, but the most glaring one is Bellatrix Lestrange, who has a very powerful obsessive love for her master, Lord Voldemort, but is still quite evil, without a single sympathetic moment to her name.
In Piers Anthony's Apprentice Adept series, the evil Tania falls in love with the protagonist Bane and has a Heel–Face Turn (and a serious personality change), though she ends marrying someone else as Bane is already married.
This trope is a biggie in the 18th-century novel Pamela by Samuel Richardson, a book that intended to be about proper conduct. A young waiting-maid's mistress dies, and so the household is given over to her son, Mr. B, who quickly sets his sights on Pamela's "virtue." She manages to refuse his advances despite his hostile behavior and attempts to full-out rape her, and eventually decides to quit and return home. Only the carriage meant to take her home kidnaps her to one of Mr. B's other estates, where she is held prisoner with her virtue as the ransom. She endures more of his advances, until finally Mr. B reads the letters she's been writing detailing her imprisonment and just then realizes what a terrible human being he's been. He lets her go, but Pamela realizes she's in love and accepts his marriage proposal. And suddenly Mr. B has been supporting an illegitimate child all this time, so he's really a good guy, honest!
In White Fang, without actually redeeming himself as he retains his wolf instincs, White Fang becomes much less wild and violent after being adopted by Scott, the only master he grows to love.
In the Sword of Truth series, both Denna and Nicci are redeemed by their love for Richard Rahl. Neither of them actually gets to be with him, as he was already with Kahlan, but Denna died shortly afterwards and Nicci clearly stated that I Want My Beloved to Be Happy.
Many fans of Tales of the Frog Princess by E. D. Baker theorize that this happened to Garrid. When you think about it, it actually makes sense. Pre-Li'l: Cold, cunning, a liar, and something of a Jerkass. Post-Li'l: Funny, relaxed, Friendly Neighborhood Vampire, very helpful ally to have around. Depending on your view, he could also have qualified as a Jerk with a Heart of Gold all along— it just took Garrid falling for Li'l for it to show.
In Death: Eve and Roarke certainly experience this from their relationship.
Played With on an ongoing basis in The Dresden Files - love can save a White Court Vampire before their first feeding, but once their demon has asserted itself, love is merely dangerous. Harry tries to invoke this for Molly Carpenter, his apprentice. He tries to avert the romantic aspect of that as much as possible (for obvious, squicky reasons), but seems to have failed as of Ghost Stories.
Turns out that it was true for Charity Carpenter as well, redeemed by her love for her husband.
Averted for Shadowman, Susan Rodriguez, and the Denarians.
Turns out that the Knights of the Cross exist to fulfill this trope, turning the hosts of the Denarians against their Fallen Angel. One of their swords is even named "The Sword of Love". Yeeesh. Don't think that they wont work with the occasional wizard who knows how to deliver the alternative for great justice.
The man that became Kthonia's husband was a Death Seeker and therefore Too Kinky to Torture. Eventually she fell for him and mellowed out.
Crime and Punishment: Raskolnikov is on his way to redemption at the end of the novel, thanks to his relationship with Sofia.
One of the most prominent themes in The Bible, with the Great Commandment in the New Testament being as love for God and love for your neighbor meaning ultimate redemption.
In The Phantom of Manhattan (a sequel to The Phantom of the Opera), Erik, the titular Phantom, realizes that his love for his son Pierre is a greater one than what he has for Christine, and when it is reciprocated he makes a full Heel Face Turn.
In Simon R. Green's book Hex In The City, a man called Sinner (who has been rejected by both Heaven and Hell, and as such must walk the earth eternally) and his succubus soulmate Pretty Poison are being attacked, and Sinner shields her with his body. As his body is being chipped away, piece by piece, by the constant attacks, Pretty Poison comprehends the notions of self-sacrifice and love, and instead moves to shield him with her own body. Cue a pillar of light that transforms her to her pre-Fall angelic state, and both are forgiven and raised to Heaven. "Come with me, to Paradise," said the angel to the man called Sinner. "For you have been found worthy, as have I."
The Fifth Wave by Rick Yancey uses this trope when dealing with Evan Walker, who is a Silencer, who basically roams the countryside shooting people until he falls in love with Cassie.
This happens to Dime Novel villain Zanoni the Woman Wizard. Arch-Enemy Dr Quartz once kidnapped Nick Carter and brainwashed him into thinking that he was an invalid married to Zanoni. Nick's kind treatment of Zanoni made her fall in love with him and reform.
The Japanned Box, a non-Sherlock Holmes short story by Arthur Conan Doyle, recounts a tutor's discovery of his employer's dark secret. In his past, the lord was a drunk and a hellion, until his since-deceased wife inspired him to reform. The titular box contains a phonograph recording of her last words, begging him not to lapse into his old ways of drinking and hell-raising. Determined to hold himself to his promise and unable to abide being pitied, the man regularly locks himself away and listens to the recording. By the time of the story, his mania for secrecy leaves his servants speculating wildly about the mysterious woman's voice they keep hearing.
In Allegiant, when given the choice between reclaiming her son Tobias's affection or holding on to power in the city, Evelyn chooses Tobias. And she's much happier for it.
In The House of Night, Stark and Zoey's relationship is entirely built on this. Initially, after he becomes a Red Fledgling, he works for the Big Bad; but after he falls for Zoey, he believes her when she tells him he can choose to be good and pledges to be her warrior.
Assault used to be a villain named Madcap, until he met the superhero Battery. They fought several times, and he genuinely fell for her, eventually surrendering to the law in exchange for (partial) amnesty for his crimes and the opportunity to be on the same team as Battery. They got married a few years later.
In the case of Regent, dating Imp is what transforms him from the Undersiders' sociopathicToken Evil Teammate into an actually marginally sympathetic and likable person. So much so that he gives up his life to save Imp's during the battle with Behemoth in New Delhi.
Twisted all around in regards to Trickster's love for Noelle. Trickster is normally a narcissistic Jerkass, but he genuinely loves Noelle and wants to find a cure for her condition. Unfortunately, it's that same motivation that drove him to become a villain in the first place, and ultimately betray his teammates for Coil. In the end, Noelle is killed with Trickster unable to do a damn thing about it, in large part because his single-minded drive to save her blinded him from potential solutions that could have.