Doing It for the Art: As has been mentioned, Day-Lewis is one of the most well known method actors around, to the point where he's actually achieved a memetic status as the go to for insane dedication to acting, as during the filming process, he never gets out of character. While playing Bill the Butcher in Gangs of New York, he famously refused to seek medical treatment for pneumonia until it became almost life threatening, as it was not in keeping with available medical treatment in the 1860's. He also ad libbed tapping on his glass eye with a knife to intimidate William Tweed. When playing a villain, he will accost other actors in character on and off the set, and get into fights in bars in preparation for a role. When playing any character, he will spend six months mastering an accent,note Even if it's completely unnecessary—the most extreme example being when he learned Czech to play the lead in The Unbearable Lightness Of Being despite the fact that the film was shot in English learning various crafts, and adopting disabilities.
Hoist by His Own Petard: His fame (or infamy) for this has cost him roles, including ones that he probably would have enjoyed doing and would have been very good in, simply because some directors (such as Peter Jackson) are unwilling to subject themselves and the other actors under their care to his behavior.
Dyeing for Your Art: Trained as a boxer for three years and broke a knuckle for his role in The Boxer.
Parental Abandonment: His father died when he was fourteen. This became an issue years later when during a production of Hamlet, he had a nervous breakdown, specifically during the scene of confronting the father's ghost, years later he admitted that he got so into the role, that he actually felt that he had seen his own father's ghost. It's his last theatrical role to date.
Playing Against Type: He doesn't exactly have a type, per se, but he first drew attention in America for playing two incredibly different roles in movies that happened to premiere in the US on the same day: as the repressed, snobbish, upper-class, Edwardian-era Englishman Cecil in A Room With A View; and Johnny, the gay ex-skinhead thug in Thatcher's London engaged in a forbidden romance with a Pakistani boy, in My Beautiful Laundrette. Many critics were impressed that he did both roles so convincingly.
Serious Business: Notoriously takes acting very seriously. Luckily he's very good at it.
He was also going to be cast as Aragorn in The Lord of the Rings films when Townshend was kicked off the project before Jackson ended up going with Viggo Mortensen. Had Mortensen actually drowned in The Two Towers film, he might've been Mortensen's replacement.