Edward Yang -- a poet of the city, whose films build up slowly but inexorably, analyzing their characters and their interrelationships minutely, patiently building tapestries made of nuance that are always more than the sum of their parts. Standouts: Yi Yi, A Brighter Summer Day, Taipei Story.
Hou Hsiao-Hsien - another leading director of the New Taiwan cinema movement, both as a historian (his trilogy, consisting of A City of Sadness, The Puppetmaster, and Good Men, Good Women) and as a chronicler of ordinary life in transition (Millennium Mambo, Three Times, Goodbye South Goodbye). Stunning cinematography, films that demand but reward patience as you watch private and public moments accumulate into the most intense cinematic experiences.
Terrence Malick -- one of the few directors dedicated to trying to touch the ineffable. Standouts: Days of Heaven, The Tree of Life, The Thin Red Line.
Tian Zhuangzhuang -- Fifth Generation director who criticisms of Communism has landed him in trouble with the government again and again. But his masterpiece The Blue Kite, his remake of Springtime in a Small Town, and his first major film September combine the most searching dramas of family life with the larger political contexts that help shape them in all sorts of damaging ways.
Park Chan-wook -- His Vengeance Trilogy, Thirst, and Joint Security Area are superb thriller classics. The kind of rollercoaster rides Hollywood always tries to provide and usually fails to.
Kim Ji-woon -- masterpieces in the Western (The Good, the Bad, and the Weird) horror (A Tale of Two Sisters) thriller/suspense (I Saw the Devil) black comedy (The Quiet Family), crime drama (A Bittersweet Life).
Akira Kurosawa -- introduced the world (or the parts that weren't already aware) to Japanese cinema. Directed maybe the greatest action film ever (Seven Samurai), the best Shakespeare adaptations (Throne of Blood, Ran), maybe the best film about a doctor ever made (Red Beard), two of the best crime films (Stray Dogs, High and Low, arguably Rashomon), and on and on. Dominated whatever genre he decided to.
Steven Spielberg -- defined cinema for generations of American filmgoers. Even with Star Wars, without Raiders, Jaws, Close Encounters, E.T., Poltergeist, Jurassic Park, not to mention the things he's produced, movies would not look the same today, for better or worse. They just wouldn't.
Hayao Miyazaki -- the best animator the world has ever produced (Walt Disney being a close second). Puts pure enchantment on film with nary a misstep. Standouts -- Spirited Away, Mononoke-Hime, Castle in the Sky, Castle of Cagliostro. All engrossing adventure stories that never, ever grow tired no matter how many times you see them. Of today's other animators, only Pixar and Brad Bird are on his level, and only when they're firing on all cylinders.
Yasujiro Ozu - devastating portraits of different generations trying to relate to and understand each other. Standouts -- Tokyo Story, Floating Weeds.