Before 1970: Vertigo (1958). I'm not particularly fond of twists, but Vertigo just works for me. I absolutely love the ending. Really, the ending makes the movie for me.
Post 1970: No Way Out (1987). I was having a hard time with the modern film choice, so I'm just going to go with this one. It pushes the believability envelope just a bit, but I still love it. It made grin and grin when I got to the end of the movie.
Sorry for the lack of details, but I'm down with a cold and not up to much more right now.