International 12th Man
You have to watch all of Cowboy Bebop, I thought the first 2 DVDs were a bit meh, but the final 4 were epic, a truly great work. Haruhi also tops, really enjoyed it, Midori No Hibi (Midori Days) is pretty decent, but too short and just ends, Haruhi is quite similar in that regard, just not enough eps to fit in the whole story. NGE is a classic, but I don't rate it that highly if truth be told. Chobits as discussed. The others I haven't seen, so can't comment.Only own anime movies (well, 1 Miyazaki and two of the Lupin series) plus Samurai X which I got free with a copy of Tenchu for Xbox.
Have seen, and some of my favourite series:
Revolutionary Girl Utena
Cowboy Bebop (haven't seen it all yet)
Samurai Champloo (as above)
Haruhi (again, see above)
Midori Days (above)
Some of the ones I watched as a child:
Recommend Cowboy Bebop, Love Hina, Onegai Teacher, Nadesico, Escaflowne, GTO, Haruhi.. Have seen many more, too many really now I come to think of it.
Robotech, so gun.