Korean movies you oughta get movies made by Chan wook park, Sympathy for Ms vengeance, old boy, Sympathy for Mr. Vengeance (this is a themic trilogy, you probably seen Oldboy, but few seen the others). Then a nice military drama (about the military border of North and South) called Joint Security Area, his debute film.
This is one director, best of them, but Korean movies are REALLY good, would recommend a slick stylistic gangster drama called A bitter sweet life.
Hongkong/China is whole another thing, hehe, would do the obvious and recommend Wong Kar wai and Ang lee movies, especially the former, great at dramas, and almost all of them starring amazing actors like Tony Leung. Their gangster flicks are pretty cool too, beside the obvious of the Infernal affairs, their best gangster movies is IMO done my a director called Johnnie To, his Election triad films is one THE best gangster films I have seen. His style is refreshing.
Japanese movies are bit more random, lots of quality stuff, but you have to wade through alot to find them, they dont have as much focused and booming film industry as China/HK or Korea right now.