"Spirited Away." If you love anime, you really need to watch something by auteur Hayao Miyazaki. In this opus, Chihiro and her parents stumble into a mysterious spirit world, where the young girl needs to work in a bath house for the gods in order to make up for her elders' faux-pas. It's equal parts mystifying and heart-warming!
"Chungking Express." The mind-product of master movie maker Wong Kar-wai, this is easily one of the best Asian movies of all time. It shows the city of Hong Kong as a neon-colored playground, rife with its own problems and overflowing with human emotion. The movie is hilarious and heartbreaking at the same time, and definitely worth a watch.
"Seven Samurai." When you have the inspiration for "The Magnificent Seven," one of the greatest Spaghetti-Western movies of all time, you know you're in for some good cinema. Seven samurai, lost without a master, take it upon themselves to avenge their disgraced lord's name with anyone and everyone responsible.