Meruem of Hunter × Hunter. He starts as a genocidal monster, who murdered his own mother right out of the womb by tearing his way out of her. He viewed humanity as something to crush, destroy and consume for his own amusement. As he plays Gungi with Komugi, he undergoes giant changes in his world view, admittingly still being a Social Darwinist near the end, but believed certain humans are worth saving and truly wanted to make a perfect world where those special people could live happily. He dies peacefully with the woman he loves, realizing in the end he was born entirely to be with Komugi in his final moments, nothing else.
There's also Neji's uncle, Hiashi Hyuuga. Starts off treating Hinata as the Un Favorite (due to her being weaker and more passive than her sister), but by part 2 they seem to be on better terms.
Kankuro also qualifies, starting off as an arrogant, Hot-BloodedJerk Ass and becoming noticeably kinder in Shippuuden, partly due to his improving relationship with Gaara.
Many people overlook it, but Sasuke did this for a short period. Team Seven managed to bring him out of his shell to the point that he was willing to die to defend them. Then Itachi scrambled his brains and he ended up power-levelling in Jerkass.
In the second half of the Shinobi World War, he gets this after having decided to go from avenger of the Uchiha Clan to protector of the Hidden Leaf Village.
Gaara himself is also one, thanks to his defeat from Naruto; as he goes from a cold-blooded, murderous sociopathic serial killer to a kind, gentle, shy and charismatic Kazekage.
While he already was Naruto's ally, Kurama takes a big level after Neji's death by going out of his way to remind a distressed Naruto of the sacrifices others made for him also because of what he means to them, even those that were caused by Kurama himself. It wasn't too long ago that a similar incident was used to the Kyuubi's advantage to persuade Naruto to release the seal...
Piccolo went from a raving, sadistic psychopath and a literal Demon prince, to one of the most levelheaded characters, all thanks to the kindness of a single child! Granted, this is probably because he only turned after he fulfilled his revenge against Goku.
Vegeta, the last remaining pure-blood Saiyan who retains their nature and pride. Once he finally turns against the one responsible for their genocide, he relocates to earth (with little choice) and grows soft in the presence of the other Z Fighters...and, after a decade or so, his wife and son. But even though his Heel–Face Turn is made official near the end of the series (because it took that long), he doesn't make it past Jerk with a Heart of Gold. He comes about as close as is possible, but he never sheds his Saiyan nature.
Perhaps the most ridiculous example is Majin Buu. He was fully prepared to just destroy the Earth and kill everyone on it... but then Hercule told him that killing is wrong. And that was all it took! Apparently, between his two previous masters telling him nothing but "kill" and "destroy", he just hadn't considered that it was immoral.
But only in the dub. That is, Chiaki J. Konaka apparently went out of his way to avoid depicting Rika/Ruki as 'cold' because 'coldness' is often attached to female characters to convey strength. She's mature and stoic, but she's not cold.
Her partner, Renamon, qualifies as well. Originally ruthless, she goes to a general Mama Bear, mostly from her relationship with Rika improving.
Yamaki is also one from the said series. From a Well-Intentioned Extremist who wants to wipe out Digimon to supporter of the Tamers in battling evil Digimon.
Guts of Berserk, upon finding Casca again and gaining new True Companions, has begun abandoning his cold, ruthless and vengeful Black Swordsman persona in favor of something resembling his original nature for the first time since the Eclipse. Mind you, he still has a rather nasty Enemy Within to deal with due to the vendetta that he was on for two years.
Gary becomes much nicer to Ash around the Johto arc after his Break the Haughty phase in the Kanto arc. By the end of the Johto arc, he and Ash finally become friends again after so many years to being rivals (which sticks when they meet again in Sinnoh).
Georgia, Iris's rival from the Unova arc, has been slowly improving, and has been consistently taking levels from Jerkass to Jerk with a Heart of Gold as the arc goes. (Her rivalry with Iris has also eased a little bit, with their bickering starting to sound a little more good-natured than either of them would probably admit.) When she shows back up for the Pokemon World Tournament Junior Cup she's improved even more, only being bitter about her loss to Iris because Iris's Dragonite beat her when it wasn't listening to commands, so technically Georgia and Iris weren't even the ones fighting.
Nami from One Piece. Gradually as the series has gone on, but especially after the timeskip. From forgiving Hachi, to immediately hugging Usopp and Chopper when they reunite, to even immediately forgiving Jinbei for letting Arlong loose on East Blue, she's come a pretty long way from the Jerkass Façade she started out with.
Not to mention, she almost never hits her crewmates anymore, starting after the timeskip. Though this maybe because of her crewmates beating her to the punch.
Also, as seen in his flashback, Jinbe was previously quite brutal when fighting against humans and couldn't care less about humans in general. His interactions with his captain Fisher Tiger and the human girl Koala and being inspired by Queen Otohime helped to change his outlook and become a more kinder person. This was very notable in that he is so far the only Shichibukai whose past changed him for the better.
InuYasha: Inuyasha, Sesshoumaru, Kouga, and Kagura all experience this at varying speeds and to varying degrees.
This is also a huge part of Mirajane's backstory. She was an Enfant Terrible in her younger days, but the shock of losing her little sister caused a massive shift in her personality, and she evolved into the guild's beloved Team Mom.
Perrine H. Clostermann of Strike Witches starts out as a Clingy Jealous Girl madly in love with Mio and openly resenting Yoshika because of how friendly the two are with each other to not only a really kind person who grows to view Yoshika as a friend and a comrade but also a really generous person more than willing to give all her funds to rebuilding her homeland of Gallia.
Initial D fans know Shingo as an asshole driver who deliberately bumps into his opponents' cars to provoke them and tried to run Takumi off the mountain pass in a last-ditch move. After said last-ditch move fails and leads to Shingo getting into an accident instead, he becomes a lot more polite when Iketani and Itsuki see him again, and in Initial D Extra Stage he's very buddy-buddy with his fellow drivers.
Fullmetal Alchemist gives us Edward Elric, who starts his series a bit of a jerk. Not greedy or cruel, but just rather selfish and myopic about his goal of curing himself and his brother, due to the crushing guilt he feels over making them the way they were, due to his own error. However, repeated exposure to the plight of others and the atrocities committed by the villains gradually make him more open and kind, so much that he's pretty well unrecognizable the the end of the story. This Character Development also makes him a Foil to the Big Bad of the series, who is essentially myopic selfishness personified.