Some actors portray characters so well that they seemingly become those characters. One of the best examples of this is Hugh Jackman's Wolverine.
It's worth mentioning that there's a difference between an actor being defined by a role because that's the only memorable role they've played, and an acor being defined by a role because they seem to become said character. Jackman has a long line of successful roles: He was nominated for an Oscar in Les Miserables. Even though Pan was kind of a flop he was awesome in it, he crushed it in The Prestige, and that scene in Swordfish everybody remembers? I mean, come on!
The man's an incredible talent and it's evident that he fully inhabits the roles he plays on screen, especially whenever he dons the claws and mutton chops for Wolverine.
There are tons of examples of actors going above and beyond and really getting into character for their roles.
He also slashed his own face and pulled out a tooth in front of his castmates.