I checked the answers here, already slapping my forehead and waiting for the inevitably list of Saw sequels and “evil swarthy foreigner” splatter and torture-porn movies. Imagine my pleasant surprise to find several of the movies I’d suggest (like Shutter and A Tale of Two Sisters) already listed and a notable absence of horny teenagers getting chopped up with an axe. Fluther really is a cut above the rest.
A few other recommendations:
Silk
Suicide Club
[REC] (the original, not the Hollywood remake)
Pandorum
Dark Water (the original, not the Hollywood remake)
Feast, Feast 2, and Feast 3 (an unusual choice, I know, but I love quirky movies, and any movie which features someone throwing a baby at bloodthirsty monsters to distract them—and plays it for laughs—is okay in my books)
The Last Winter
The Shining (Kubrick’s version)
The Thing (Carpenter’s remake)
Nosferatu