Shutter Island may be my favorite Scorsese film which isn't necessarily a popular opinion considering that The Wolf of Wall Street is his highest grossing and there is of course Raging Bull and Taxi Driver. The last scene in the film is what really seals the deal for me. Teddy, Leonardo DiCaprio's character asks, "What would be worse? To live as a monster or to die as a good man?"
The premise of the film is that Teddy is a cop in the 1950s who, along with his partner Chuck (played expertly by Mark Ruffalo) is investigating the disappearance of a patient named Rachel Solano at an insane asylum on the titular Shutter Island. It turns out to be a case of the inmates running the asylum, as Teddy turns out to be a patient there undergoing a kind a of therapeutic role-playing where his doctor, posing as his partner Chuck, is attempting to get him to realize that he's killed his own wife (Michelle Williams) in revenge for drowning their children.
Teddy final admits that his real name is Andrew Laeddis - not Edward Daniels - and that he did in fact murder his wife in the 1952. She was not a victim of a fire as he has conjured in his mind and Rachel Solano was never missing to begin with. The monster/good man paradox is relevant because Teddy is slated to undergo a lobotomy which his doctors have been trying to avoid. As people in the modern era, we know what lobotomy means - it is in fact a kind of death - death of one's personality and everything that makes a person themselves.
Teddy's final question makes the audience question if he does believe someone else killed his wife or if he has finally admitted the truth to himself. He seems to indicate to Chuck that he doesn't want to live as the monster who killed his wife, but instead chooses to "die" a good man by undergoing the lobotomy and not admitted that he is Laeddis.