Any movie with Mifune Toshirou in it! This includes: Yojimbo, Sanjuro, the Hidden Fortress, Samurai Rebellion, Chushingura, Seven Samurai, and about a hundred others, but these are my main recommendations.
Most of the ones listed here were directed by Kurosawa Akira. Film buffs, especially Japanese film buffs, should make sure they watch one or two Kurosawa films.
I went on a major classic Japanese cinema binge right before I met my current boyfriend of 3 years. Mifune came up in conversation on our first date, and I think that's how we knew we were made for each other! :)