My favorite series are: Neon Genesis, Initial D, Lain, and Cowboy Beebop. Honorable mentions to Wolf's Rain, Texhnolyze, Haibane Renme and Full Metal Alchemist. Also liked Fooly Cooly and Paranoia Agent, though they were both pretty weird. I've seen most of Inuyasha also and I liked it at first, but it got a bit tired after a few seasons. The Inuyasha movies are decent though.
Those who haven't seen the series, check out the Cowboy Beebop movie (has nothing to do with cowboys...). You don't have to have any knowledge of the series to get the story and I really enjoyed it.