Favorite anime? Mine are Serial Experiments Lain, NANA, and Nodame Cantabile.
But I also like FLCL, Cowboy Bebop, Paranoia Agent, Elfen Lied, One Piece, Honey and Clover, Outlaw Star, Minami-Ke, Lucky Star, Gundam Wing, Gundam SEED, Gundam SEED Destiny, Neon Genesis Evangelion, BECK: Mongolian Chop Squad....this list is becoming long so I'll stop.
Basically my favorite genres are Sci-Fi and Romance/Slice-of-life.
The first anime I ever watched was what everyone usually starts out with: Sailor Moon and DBZ. Then everything on Toonami. Then later I moved on to titles aimed at young girls like DNAngel and Fruits Basket (the anime is fluffy and light, the manga is much more mature). And then I'd say I started watching it all the time.
I love Japan for giving us anime. I love the USA for giving us indie comics that are more diverse and engaging than most manga I've read (but in a different way....manga usually lacks subtlety and is heavy on over-exaggerated gestures and scenarios while western independent comics have a lot more subtle humor and character development.)