The anime films suggested above are great, just want to add Steamboy and the Ghost In the Shell films to the list, especially the second one, Innocence, easily one of the most beautiful films I've ever seen. Also Tekkonkinkreet, one of the most visually unique and emotionally stirring animations ever made.
Some live action suggestions below:
I didn't like Ichi the Killer much, though I generaly like that director's work. He's totally insane, makes a kids film one month and a blood-soaked horror the next. Stuff of his I liked include Gozu, Shangri-La, The Great Yokai War, Visitor Q (if you've got a strong stomach) and the Happiness of the Katakuris. The Dead or Alive films by him are also supposedly good, but I haven't seen them.
Also check out films by Takeshi Kitano. His Zatoichi was awesome, Dolls was beautiful, and his old gangster movies are all good fun. Blood and Bones wasn't directed by him but he stars in it, and it was superb. Sort of like a Japanese version of There Will Be Blood, but Kitano manages to get a bigger range of emotional response from the audience than Daniel Day Lewis does while only speaking about 1/10th the number of lines!
For some fun sword-wielding action check out Red Shadow, Aragami (shot in only a week, Casshern (gorgeous-looking film, live action adaptation of some old superhero anime set in a post-apocalyptic world), and maybe Azumi.
Also a hillarious film I saw a year ago called Dai-Nipponjin, it's a mockumentary about a superhero who's not all that brilliant at what he does and his personal life is falling apart. Really side-splitting, it's what Hancock should've been like!
Lots more that I can't remember off the top of my head.