I am a -huge- fan of the Studio Ghibli collection - with my favourite being Spirited Away. as for anime, well there's very little of it on mainstream TV over here in the UK, but I've seen shows such as Wolf's Rain, Bleach and Full Metal Alchemist and rather liked them.
Whenever I'm over in the USA I make time to watch Adult Swim, I've come across most of the stuff I watch through that
hmmm...there's so many great animes out there. its hard for me to pick. however, i can list all the animes i love are dragon ball, dragon ball z, inuyasha, full metal alchemist, ghost in the shell, code geass, gundam wing, yu yu hakusho, bleach, naruto, and cowboy bebob. those are my favorites so far.