Also, Edmund. He starts off as a Jerkass in The Lion, the Witch, and the Wardrobe, but slowly becomes less selfish as he's captured by the White Witch and realizes the damage he's caused. He ends up making a Heroic Sacrifice (of which he gets better) to break the Witch's wand (which turns the tide of battle in the favor of Peter's army, since it keeps the Witch from turning their soldiers to stone). In Prince Caspian, he is the only one of the siblings who remembers that Lucy's Cassandra Truth about the magical land in the wardrobe was right, and thus knows she's probably right about the other stuff she claims and does whatever he can to support her.
Ronan Lynch starts out as a brooding, violent, selfish punk who has frequently been described as "cruel." Calla even calls him "the snake." He frequently makes rude comments, mouths off to everyone, and even Adam can barely stand to be around him for most of the first book. In The Raven Boys he does about two nice things: adopting Chainsaw and punching Robert Parrish in the face. Come the second book and we see his genuine love for his family and his friends and he becomes a lot more considerate and helpful to others while being shown to have a strong moral center. A healthy dose of POV chapters and CharacterDevelopment will do.
Granted he's still violent, brooding, cruel, and closed off. He he just gets a bit better about it. Unsurprisingly, by the second book he became a huge fanfavorite.
Happens a lot in the Chalet School series. Girls who start off as bitchy, sulky or standoffish will often come to learn the error of their ways and become nicer people after being introduced to the ways of the school, or getting a good ticking-off from one of the mistresses. And if that doesn't work, there's always a handy accident; for instance, Eustacia Benson injures her back after running away from the school, is confined to a wheelchair for some time and becomes a much nicer person.
Peter Pan in Scarlet takes it for granted that Slightly, formerly a condescending, cowardly little snob, grew up to be kind, sensitive and "as gentle as a lamb". Of course, the original novel and the various drafts of the play implied that Slightly had his ego brought down to size after the boys left Neverland, and in Peter Pan in Scarlethe's recently been widowed, so suffering probably sweetened him a little.
James Potter started out as a huge Jerk Jock and then eventually became Head Boy in his seventh year. This alone can't signify redemption - Percy was Head Boy, and he disowned his family two years later - but he then marries and dies for Lily Evans.
There's also Dudley Dursley. He spends the first five books growing up to be a spoiled bully who led a gang of delinquents and beat up other children. After Harry saves him from a Dementor, he makes several honest (if awkward) gestures of friendship, including leaving a cup of tea for Harry and saying that he doesn't think Harry is worthless.
Draco Malfoy goes through a rather subtle example in the last few books. For most of the series he's a bully who constantly tries to make life difficult for Harry and uses his father's wealth and influence to have his way. After he foolishly leaps at the chance to join Voldemort and spends the sixth and seventh books learning that he and his parents are constantly in danger of outliving their usefulness, he (and they as well) drop all interest in supporting Voldemort and his plans for pureblood wizard supremacy and focus instead on the family getting through alive. This includes a point in the seventh book where Harry and his friends have been captured and brought to the Malfoy Manor and Malfoy is asked to identify them. While it's implied he can tell who it is, he only says that it "might" be Harry, Ron, and Hermione and that he can't be certain. The epilogue shows him nodding at Harry as they see their kids off for Hogwarts and Word of God says that he raised his kid to be better than he was.
Matteo in Someone Else's War, who goes from a snobby, condescending brat to a loving young man who will risk his life and compromise his ideals if it means saving his friends.
The title character of Artemis Fowl gradually does this over the course of The Arctic Incident, The Eternity Code, briefly reverting because of a mind wipe, and finishing the transformation in The Opal Deception.
From Michael Grant's cult-followed GONE series, Diana Ladris starts out a manipulative, lying, apathetic sociopath, and slowly moulds into the token good teammate of Caines team and eventually does a heel face turn and joins the protagonists in FEAR it doesn't last long. Only took her five 600-page books, too.
Blackstar also, believe it or not. While Onestar becomes more of a jerk as the series goes on, Blackstar (a gruff battle-scarred cat) becomes something like an old kindly veteran who still has a gruff side.
Taran, of the Chronicles of Prydain, goes through several levels of kindness, thanks to massive amounts of Character Development. In the first book, he's a whiny Designated Hero who gets into trouble, is rude to Gurgi and Eilonwy because they annoy him, and tries to attack Flewdry Flam with a sword simply because he was expecting someone else to be waiting for him. By the end of the series, he has become far more patient and kind, proving himself to be worthy of the title of High King.
Like the above example, Trini of A Brother's PriceDoes Not Like Men, and for good reason, but when she gets married she is perfectly kind towards her husband. Much of her initial rudeness towards him is due to suspecting he might be like her deceased husband.
A New Dawn: Kanan starts off the book callous and deliberately uncaring about anyone except himself. By the end he's softened greatly, and the eventual results of this are seen six years later.