Adaptation (kinda gay at first, but it gets really weird really quickly)
Vanilla Sky (yeah, yeah, yeah, Tom Cruise, but who doesn’t like a mystery film that ALSO shows Penelope Cruz’s tits?)
Touch of Evil (an Orson Welles classic. I think are there two versions available; get the Director’s Cut)
Brick (How could I forget Brick? One of the most creative movies I’ve ever seen. Think old-school film noir along the lines of the Maltese Falcon or Rebecca, but with color.)
The Manchurian Candidate (the original, not the one with Denzel)
The French Connection (not really a mystery, per se, but it’s entertaining and has a good plot, which brings me to the film that inspired The French Connection’s chase scene):
Bullitt (Steve McQueen and a Mustang with a fucking 390 in it flying around SF? What more can you ask for?)
The Jason Bourne trilogy is really good, but you’ve probably already seen them.