Haha, the title of your thread reminds me of the Bill Parcells press conference when he said at practice his ofensive coordinator likes to throw in "a few Jap plays...no offense to the orientals" You may want to reconsider as this is generally considered a slur...just a thought.
Now in answer to your question. These are all live action Asian flicks (not all Japanese):
Takeshi Miike: (in addition to the ones Moby mentioned)
* Ichi the Killer - very disturbing
*Visitor Q
Three Extremes - 3 short films that are all compelling and shocking (Moby, if you like Miike, you should check this out)
OldBoy - Korean revenge flick that is absolutely awesome
A bit more mainstream:
Hero - one of the most visually stunning movies i have seen.
Kung Fu Hustle - hilarious
Shaolin Soccer - same guy that did Hustle. Funny
For truly classic amazing cinema. You have to check out some Kurasawa. All are good, but I highly recommend:
Seven Samurai - the quintessential samurai flick. simply a masterpiece
Rashomon - cool story telling. A murder is told from several character's point of view.
Ikiru- amazing story about a beurocrat who develops cancer and changes the way he lives the remainder of his life
Yojimbo - bad ass samurai flick - it was remade as Western - A Fistful of Dollars
Sanjuro