I don't particularly prefer any genre, I just watch them for the "big kid" factor. If the show lets me sit back and relax and makes me what to see more of it I will. I don't want to have an aneurism just trying to work out what's going on, a la Neon Genisis towards the end.
All of the Studio Ghibli anime's I've seen have done just that. Laputa, Nausicaa, Spirited Away, Kiki's Delivery Service & Howl's Castle all just made me sit back and want to watch them. Grave of The Fireflies just blew me away , using an anime to deal with such a sensitive subject and doing it so well.
I prefer to listen to them in original Japanese with subs. To me the american dubs just don't seem quite right. Enough waffle and on to the list
As well as the above mentioned movies my list of favourites in no particular order is:
Gunslinger Girl.
Got hooked right from the first episode. You never really knew which way it was going to go.
Project A-Ko
An oldie but a goodie although I'd take A-Ko or B-Ko over C-Ko any day
Mezzo.
You just gotta luv orange jumpsuits
Madlax.
Wierd but you just had to keep watching to find out what the hell was going on
R.O.D the TV.
Gives a whole new meaning to paper cuts!
Maburaho.
What more could a boy need than a school full of luscious lovely after him
Ikki Tousen.
Enough "booby bombs" for any self respecting pervert
Macross
What more can you say.