Definitely A Tale of Two Sisters, brilliant film. And the war film mentioned too.
Akira Kurosawa(the ones mentioned already), plus Throne of Blood, and High & Low are fantastic too.
Try some Takashi Miike films too, I recommend Rainy Dog, The Bird People in China, Sukiyaki Western - Django, and Ley Lines.
Sympathy for Mr Vengeance
Oldboy
Sympathy for Lady Vengeance
A Bittersweet Life
The Good The Bad The Weird
Memories of Murder
The Host
Infernal Affairs 1,2 and 3
Public Enemy
Hero
House of Flying Daggers
Flashpoint
SPL
Most Takeshi Kitano films, Hana Bi is one of his best
Battle Royale
Any of the Studio Ghibli anime films
I'm a Cyborg, But That's Ok
Joint Security Area
Alone
Ringu
Shutter
The Big Swindle
Chocolate - brilliant film from the makers of Ong Bak
The Eye
Bangkok Dangerous
The President's Last Bang
The President's Barber
Shiri
Most films by Kim Ki-duk
The Quiet Family
Try Wong Kar Wai films like Chungking Express, Ashes of Time, As Tears Go By and so on
Protege
Confessions of Pain
The Returner
Blood Brothers
Purple Storm
Purple Butterfly
Bright Future
The Banquet
6ixtynin9
New Police Story
Re-Cycle
Sharkskin Man and Peach Hip Girl
Koma
20 30 40
Last Life in the Universe
Zatoichi(the 2003 release version)
Electric Dragon 80,000 V - just has to be seen
Just a few I liked that I can think of.