I like a lot of different stuff. Everything from 80's action (just for the hell of it) to old silent stuff like nosferatu. I never see much movies thats not at least 5-10 years old though. There's more total crap than good stuff coming out these days...
I like Star Wars a lot too, mainly the old trilogy but also episode III. I and II were medicore at best imho.
I watch some anime stuff too, but not much. Ghost In The Shell and Akira would have to be my favourites from that genre.
I'd say my favourite for the moment is the Lynch stuff, especially Mulholland Drive, Blue Velvet and Twin Peaks.
And of course all the strange Norwegian stuff like Svidd Neger, Johhny Vang, Den Brysomme Mannen and Naboer. What is it with Norwegian films and weird men ? :P