My all time favorite Japanese films are the Yakuza Papers: Battles Without Honor And Humanity. It's a 5 part feature film series that covers the growth of the Yakuza from WWII through to the 60's.
Here's a montage that some dude made on youtube featuring footage from all 5 films set to some random music that has nothing to do with the movies.
They were directed by Kinji Fukasaku (Director of Tora! Tora! Tora! and Battle Royal) and many people consider them to be the Japanese mafia equivalent of the Godfather series.
city of the lost children, any Akira Kurosawa movie, The Vengeance Trilogy: Sympathy for Mr. Vengeance, Oldboy, Sympathy for Lady Vengeance. There are so many good foreign movies. what are you looking for? comedy, romance, action, horror?