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.
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 The Bully 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.
Granted we know little about his and Lily's past, so calling him The Bully is a stretch.
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.
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.