HUGE anime nerd, here...have some suggestions!
If you like robots or dogfights:
Macross Zero (macross with 3d computer rendered mech fights)
Zone of Enders
Eureka 7
Battle Fairy Yukkikaze
Appleseed (there's an old one and a new one, both are good, the new one is primarily computer renders other than a few hand-drawn cutscenes by the guy who animated the old one. Personally I recommend the new one HIGHLY, if for no other reason than the first 10 minutes is a cool fight scene. And by cool, I mean totatlly sweet.)
If you like fight scenes:
Samurai 7
Noir
Afro Samurai (american production, samuel l jackson does some work, REALLy good for american 'anime')
Scrapped Princess
If you like Cowboy Bebop:
Coyote Ragtime Show
Eureka 7
If you like something strange, but hilarious:
FLCL
Guu (full title is "Jungle wa itsumo, hale noche Guu", translated "The Jungle was nice, then came Guu". This is probably the strangest anime EVER, but well worth a watch)
Ebichu the housekeeping Hamster (LOTS of perversion in this one, don't watch it around kids)
SD-Gundam (Gundam, with all the characters in super-deformed cute mode)
If you like story:
ANYTHING by Studio Ghibli (Princess Mononoke, Steamboy, Howl's Moving Castle, Spirited Away, and some others).
Samurai 7
Anything with the names Captain Harlock or Queen Emeraldas in the title
Anything in the Harlock/Emeraldas/Galaxy Express universe (Galaxy Express 999 and it's sequels, and the newer series Galaxy Railways)
Scrapped Princess
I dunno...there's TONS more...feel free to ask me about any of these or for other recommendations...these are just the ones that came up as the best off the top of my head. There are other PHENOMINAL anime out there that I've seen that I'm just drawing a blank on names for... heh