Arlington Road - 1999, starring Jeff Bridges and Tim Robbins is an awesome mystery / thriller, well worth a look.
Marathon Man - 1976, Dustin Hoffman, Lawrence Olivier, Roy Schieder.
Some unforgettable scenes in this and great performances all round.
Out Of The Past - 1947, Robert Mitchum, Jane Greer, Kirk Douglas.
Absolute classic film noir mystery, thriller. If you liked LA Confidential you should like this. Kirk Douglas is at his best in this, just a pleasure to watch.
Agree with the Hitchcock choices, especially Rear Window and the original 39 Steps. A lot of the old film noir stuff with Bogey and the like are usually good value too like The Maltese Falcon and The Big Sleep.