I agree with you on Saw. Some people think the story is just an excuse to show the torture scenes, but I think it's the other way around - the gruesome scenes are to entice people into going to see a thought-provoking story.
I thought Dead End, made in America by a couple of French film makers, was a good one - scary and you wonder what the hell's going on right up to the end.
You've probably seen these, but Seven, The Others, and Hide & Seek are all good ones that keep you thinking. Also, some of the older David Cronenberg ones - Videodrome in particular. I would also recommend the original Dawn of the Dead and Night of the living Dead. And that Johnny Depp one - can't remember what it's called - about the guy with writer's block.
I don't know if this is the kind of thing you are asking about...
Edit. The Johnny Depp one is Secret Window. And Robin William's One Hour Photo is a good thriller.