You gotta see some asian films. Some of the best films I have ever seen came out of Asia. Here's an awesome list:
Oldboy (as someone mentioned)
Lady Vengeance (which is part of the Vengeance trilogy. Oldboy belongs to it too.)
A Tale of Two Sisters
Time (this movie is nuts)
A Bittersweet Life
Cello
Koma (some blood)
Diary (also known as Mon Seung)
Re-Cycle
The Eye (Gin Gwai)
The Eye 2 (Gin Gwai-2 the original Eyes not American remakes)
Shutter (original)
Premonition
Suicide Club (cult classic in Japan. Has an interesting message at the end. Warning: bloody movie)
Noriko's Dinner table (sequel to suicide club. I found it really interesting.)
Tomie movies (based off of Mangas by horror master Junji Ito. Old cult classics)
Pulse (Kairo. Original)
Audition (bloody towards end)
Anywho, there is a small list to get you started

. Just so you know most of those are horror thrillers but I usually watch movie without blood and gore since I think it's unnecessary. Only the ones noted are bloody but are worth enduring for the story.
Happy watching!
Edited by KNash, 14 April 2012 - 06:38 AM.