My favourites, some already mentioned, + my fave movie by that director:
Lars von Trier. "Breaking the Waves" Coen Brothers. "Barton Fink" Wes Anderson. "The Royal Tenenbaums" Terry Gilliam. "12 Monkeys" Zhang Yimou. "Shanghai Triad" (screw you, I like it) Jim Jarmusch. "Night on Earth"
Ah, this is hard. Lots of directors I like, but I'm either not familiar enough with their films to call them "favourites," or I think they have one or two good movies, the rest being ehhh. (Think Kevin Smith.) Ah, well.