Oldboy is a film with a twist that feels more organic within the film, than just a 'Hoo-haa! We got you!'-The Game/Fight Club/Haute Tension-style twist.
I also loved the subtle unpredictability of Eyes Wide Shut. It doesn't have a big-reversal moment, but rather a constant feeling of 'is this real, or is it all a dream?'.
The master of twists was Hitchcock and his best twister is probably, 'Psycho'. Honorable mention should also go to Jacob's Ladder and the original Planet of the Apes.