Some of my favorites, in no particular order, are:
Lain, Nadesico, Neon Genesis Evangelion, Kodomo No Omocha (Don\'t judge me!), Crest of the Stars (Including the follow-up serieses), Grave of the Fireflies, Patlabor, Bubblegum Crisis (and 2040), Boogiepop Phantom, Betterman, Ninja Scroll, Monoke Hime, Cowboy Bebop, Ghost in the Shell, Blue Seed, Ah! My Goddess, and Macross (not the same as Robotech).
I also have the first 2 DVDs to .hack//SIGN, and it looks to be good so far.
Its a pain trying to collect all these series on DVD, though; anime DVD costs are insane, at the moment, but I do have most of those serieses on VHS, so no huge loss.
My best friend had a strange Tenchi fixation when they first started airing it on Cartoon Network, something I never quite understood...