some i recommend, in no particular order:
Death Note (really great intellectual tension)
Code Geass (also has great intellectual tension)
FLCL (kinda crazy-random but cool. short and sweet)
Elfen Lied (i really like the intro song for this)
Blood+ (long and violent with a deep, heavy story)
Serial Experiments Lain (at times confusing, but great)
Tengen Toppa Gurren Lagann (name sounds really strange and kinda stupid to me for some reason, but it's quite exciting and very fast-pace)
Samurai Champloo (really well-done fights, in my opinion)
paprika (dream manipulation shenanigans)
nausicaa of the valley of the wind
howl's moving castle
kiki's delivery service
a lot of anime is total crap, but even when really crappy it apparently appeals to the masses for reasons i will never understand.
a lot of the better-known is really cliche and has bad writing or is stupidly and sickeningly cute or is otherwise just ridiculous in every way.
also, Bleach was pretty good earlier in its days but it's unbearably drawn-out and is plagued by random terrible, non-sequitur episodes
i've apparently watched a lot of animes. I don't really care what medium a good story comes in, but i guess i've just had good luck finding animes that appeal to me. maybe they will also appeal to you.