Let me add a few more movie titles to this thread.

Oldboy - Drama about a man held prisoner in a hotel room for 15 years. He's released and must find out why. Directed by Chan Woo Park(JSA)

Three... Extremes - A trilogy of horror movies from Takeshi Miike, Chan Woo Park and Fruit Chan.

Infernal Affairs - A Police/Triad thriller/drama. About an undercover cop in the triad and a mole on the HK police force. Parts 2 and 3 are good too.

Azumi - From the Director of Versus an adaptation of the manga.
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Pain or damage don't end the world. Or despair or fucking beatings. The world ends when you're dead. Until then, you got more punishment in store. Stand it like a man... and give some back.