Favourite movies, wow. I don't watch many these days, but I used to watch a reasonable number. Bunch of Ghibli of course, mainly Whisper of the Heart, Totoro, Kiki's and Nauisicaa, although they're all good. Akira, Milennium Actress, GitS, etc. All the usual stuff.
Western animated stuff too. The Book of Kels is amazing. Mary and Max will make you cry. Edison & Leo is hilarious, if hard as hell to find.
Old stuff like Danny Kaye's work (I've seen The Inspector General how many times?), Topper, Death Takes a Holiday, Nosferatu, silly as it is. Young Frankenstein. 2001: A Space Odyssey of course, with the sound turned up.
An assortment of other stuff. The original Star Wars trilogy, even-numbered Star Trek films, the Scott Pilgrim movie, Battle Beyond the Stars (total guilty pleasure), Stop Making Sense (the best concert movie ever), The Princess Bride and probably a hundred I can't think of off the top of my head.
That's a good start I guess.