[Despare]

Give 3 Extremes a go too, fun stuff. The list goes on and on but if you're into classic films (heh) check out Onibaba and of course you know about Akira Kurosawa's stuff right? Gozu, Zatoichi, hell if you want some kung fu action check out the Kung Fu Hustle and 5 Deadly Venoms. Netflix ALL of those... now. If you're looking for a good asian war film don't miss Tae Guk Gi: The Brotherhood of War, I LOVED that movie.
Don't miss Oldboy or Sympathy for Mr. Vengance either. Or Roshomon. Dammit I'm naming too many; this is my last edit.

Oh, I'm sure a lot of people will tell you to check out Audition which is fine because it's a good film but I thought Tale of Two Sisters was better, get that one as well.

More Asian films to check out (mainly in the horror genre as the list would be too long with all genres).

Aragami
2LDK
Versus*
Suicide Club
Izo (not so much horror as WTF)
Stacy
Wild Zero (both Stacy and Wild Zero are over-rated though)
Junk
Biozombie (also over-rated)