Spike, more so through seasons 5-6. While his love for Buffy started out as a creepy obsession, he genuinely became a nicer guy around after the time Glory tortured him, and it more or less continued upwards, especially after he regains his soul in 7. He's still a total dick to Angel, though.
That woman you might have seen chilling in prison on another show before breaking out to save a villain? Who's treated by some of the characters as so cool and nice now? Faith. Yeah, that Faith.
Zig-Zagged with Cordelia in Season Three when Xander cheats on her, effectively ousting her from the Gang. Cordelia attempts to return to her old ways, but Harmony has usurped her position and shut the door. Cordelia returns to aid the Scoobies in the Season Three Finale. Her move to Angel cements her growth as a caring person.
In Angel, Faith. She becomes even kinder and more morally centered than before her Face-Heel Turn, to the point where some fans claim Faith is better, gooder than the rest of the cast.
A mix of this and Took a Level in Jerkass with Pierce. In the first season, Pierce was an ass, but his role was mostly as comic relief. In season 2, he becomes an outright villain, but he also becomes more sympathetic and develops more of a Freudian Excuse.
When he first appeared in the Criminal Minds episode "Profiler, Profiled", Detective Silenski was a racist, condescending Smug Snake who spent the majority of his screentime insulting and belittling the BAU. When he reappears in "Restoration", he's cleaned up his act considerably.
The Doctor. Yeah, you might know him now as a goofy fun-loving guy who likes to save innocents, but his first incarnation wasn't nearly as nice. His very first story featured him kidnapping two humans because he didn't want them exposing his secret, and he often showed no qualms about killing people they encountered. Part of the change was definitely deliberate, as the writers wrote him becoming softer and kinder over his run, but part of the change is due to the change of the show's premise. When the Doctor started out he was a mysterious presence to intrigue the viewers and the show's real protagonists, the companions Ian and Barbara, whereas now much of the Doctor's back-story is known, and he often functions as the main hero.
** Note that the Jerkass persona can be chalked up to Early-Installment Weirdness: the Doctor is only downright malicious in his first three stories and softens up afterwards, and his negative traits almost entirely disappear by the end of his first series. William Hartnell spends most of Season 2 playing an eccentric loveable grandfather figure who is constantly giggling and calling people "my dear boy". As evidenced in "The Waters of Mars", nasty things happen when the Doctor doesn't have a companion. Maybe the Doctor needed Ian and Barbara's influence to take a level. One Eleventh Doctor comic featuring Ian as companion had the Doctor explicitly say that Ian and Barbara were his influence to become a prosocial force rather than just a selfish old man with a time machine.
Romana decides to spontaneously regenerate to serve as a symbolic change for her doing this. Her old self was smug and a bit of a pain, but when the Doctor's influence on her character made her realise this was not a good way to be, she regenerated into a new body in which she was a lot more amiable and something of the Doctor's Distaff Counterpart.
Lady Mary and Lady Edith in the second series of Downton Abbey. O'Brien similarly becomes much nicer due to residual guilt from the horrible thing she did to Cora.
Over five seasons, both Blair Waldorf and Chuck Bass on Gossip Girl have gradually become kinder and more accepting. Both are still quite sarcastic and snarky, but they're no longer deliberately malicious or cruel. At least Chuck isn't. Blair followed this trope until somewhere during season four when she turned around and Took a Level in Jerkass instead.
The prime example will have to be Patricia, who was originally a total bitch to Nina (for thinking she hurt Joy somehow, mind you) but, after learning to trust her, became much nicer, despite still being rather tough and sarcastic. Even in other seasons, when she finds new people to hate, she never goes to the same level she did for Nina, showing she did in fact change.
Jerome. Oh, Jerome. At first a manipulative and uncaring, he eventually showed a much better side to Mara when she got to know him, and this put him on the path to becoming a better person. Case in point- in the first season, he allied with Rufus out of jealousy of Sibuna's closeness. In the second season, he started helping Rufus again- to rescue the kidnapped Trudy and find the stolen gem. He took another level in jerkass in season three though.
Ziva David from NCIS has in the past couple of seasons evolved softer qualities including a big sister instinct for McGee. Though it may be those aspects of her personality were always there and she needed to feel at home on the team.
Once Upon a Time puts an interesting spin on this, where characters when introduced are very kind and caring, but subsequent episodes show them to have been cruel and petty in the past.
When introduced Snow White's mother, Queen Eva, seems like an archetypal version of The High Queen. It's then shown as a teenager she was a Rich BitchSpoiled Brat, who took an opportunity to humiliate Cora just because she could. Twice even. This bit her in the ass hard.
Snow White herself was a bratty child once too, with a high sense of superiority. Her mother scolded her for it, and insisted it change. By late Season 3 she freely admits she was a bratty child, which Regina instantly agrees with.
Jefferson, The Mad Hatter, is shown to be friendly man and loving father, who is totally screwed over by Regina. It then turns out that years ago, he quite cheerfully participated in the Break the Cutie and Corrupt the Cutie that Regina was subjected to, which turned her into the Evil Queen. This has the added bonus of her treatment of him come off as rather karmic.
Eventually both Regina and Rumplestiltskin get this, as Love Redeems.
Larry "The Kube" Kubiac on ''Parker Lewis Can't Lose," who went from a typical bully to a far nicer character that mostly got along with Parker and friends as early as the middle of the first season. One episode even shows that he only plays up the "Bully" role because that's how most people view him, but he's actually a pretty good guy.
The Klingons went from bad guys to Good Is Not Nice between TOS and TNG. The final TOS movie shows us how. However, it's disputable how much they've changed really when it comes to conquering: they're chummier with the Federation, but they may well be no different to other races.
From a specific episode of the original, Elaan from "Elaan of Troyius".
In Wizards of Waverly Place, the case is arguable for Alex since she grew more evil, but she does grow more responsible and bit more caring too. An example is when she is put into Larytate's Happy Helpers's she finds are a joke and actually turns the club into something that actually is helpful.