The original Wicker Man is pretty amazing, imo. It's a psychological thriller (but it has no actual "scare" moments, it's all atmosphere really), but it does have some sexual content if that sort of thing bugs you.

Pi: Faith in Chaos is one of my favourites, and A Tale of Two Sisters (but god, the original Korean version, please). Both are thrillers; Pi psychological and Tale being a more classic ghost story (and also the sort of movie you have to watch twice to get the full effect of).

THRILLERS ASIDE.

If you haven't seen them already: Both Vampire Hunter D movies (though the second is much better; the first one shows its age and seems cliche now even though it was novel at the time), The Abyss, Grave of the Fireflies, Akira, Full-Metal Jacket, annnd...I'm not sure I'd recommend A Clockwork Orange because I walked out of it going "I want that 90 minutes of my life back," but it's definitely something else.