nowadays, asian movies are really gaining popularity not only in asia but in the US as well...
here are my faves:
korean - my sassy girl, il mare, the classic, windstruck, taegukgi, ditto, joint security area
chinese - crouching tiger hidden dragon, hero, house of flying daggers, curse of the golden flower
japanese - memoirs of a geisha, the last samurai (not really japanese but japanese-inspired)