What lesser known movies have twists that blew your mind?

We all know about movies like Psycho, Memento, The Sixth Sense, and The Usual Suspects, but are there some films people don't talk about as much that also have those kind of twists that leave the audience shocked?

Other famous movies that always come up I can think of are Shutter Island, The Crying Game, The Prestige, Atonement...these are tried and true. I'd love to be surprised by some more unknown films.

Edit: Thank you for all the suggestions, folks! I can't wait to try some of these!!!