Any movie by Satoshi Kon (RIP). This man was a cinematic genius. Not only the montage, mise-en-scene of his movies are top-notch, but also all of his movies have meaning and messages that can make your life better. My favorite one is Perfect Blue.
Wolf Children. Werewolves are my favorite monsters of all time, and this movie not only has a very interesting take on it, but also managed to create a very poignant story.
I'm a fan of cyberpunk, so GITS and Akira are naturally some of my favorites.
I don't like Studio Ghibli very much. I think they're very overrated. My favorite movie there is Whisper of the heart, because it talks about being a young artist, the relationship between art and depression, etc. I also like Grave of the Fireflies. The movie that Miyazaki's son, Goro, made is one of the worst movies ever made. And Myazaki, the father, is overhyped.