I collect a little, but I'm pretty picky. I like good animation, a solid plot, and interesting characters which rules out most of them, LOL.
My collection consists of a bit of Ghibli stuff (Spirited Away, Princess Mononoke, Nausicaa, Pom Poko) as well as Escaflowne (series and movie), Serial Experiments Lain (rich and brilliant mindgame stuff), and Blue Sub 6. Have watched a lot of other stuff and didn't care for most of it...we used to do an anime night once a week here and friends would bring over different stuff so I've seen quite a few things but haven't committed them to memory.
I also have a weakness for AMVs and have lots and lots of those.