V for Vendetta - gives you another perspective on terrorism and Hugo Weaving's performance is absolutely stunning
The Bicentennial Man - a very little known film, but raises a lot of questions about artificial intelligence and when a robot can become a human, 'As a robot, I could have lived forever. But I tell you all today, I would rather die a man, than live for all eternity a machine.'
Seven Pounds - How guilt and love can push you to do amazing things, both wonderfully sad and beautifully uplifting at the same time.
I would agree with others mentioned in this thread like Garden State, Requiem for a Dream, Into the Wild, The Machinist and No Country for Old Men - all immense films. Also, Little Miss Sunshine, Moon, the Hurt Locker