If you want some good stuff that doesn't revolve around action, these are recommended:
-Kimi Ga Nozomu Eien (love triangle story. Very good stuff)
-Koi Kaze (if you can stomach certain masturbation scenes in episode 4-5, you'll be treated to one of the most atmospheric and emotional animes out there)
-AIR (Another series drenched in atmosphere about a young man who comes to a town with his little puppet, meets a girl, and all kinds of strange, sad and wonderful things happen. Absolutely stunning visuals)
-Haibane Renmei (Something very different about people with wings and life in general)
Series with action:
-Elfen Lied (super cool series about a new race of super humans and their encounters with a normal boy and girl)
-Scrapped Princess (Medieval setting road series that manages to be funny, serious and cool all at the same time. First half is great, second half not up to par (but you'll most likely want to watch it anyway)
I could go on and on, but I won't. I can't end this without mentioning something with giant robots in it, though, so here goes:
-Neon Genesis Evangelion and RahXephon. Both should really be watched.
.. I figured we were only mentioning R1 releases, but I guess that never seems to stick.
