anime for the anime n00b?

Absolutely nothing to do for the next 3 weeks, so I've decided for the first time ever to delve into the world of anime.
What's really popular out there?
What are your favorites?
How would I go about watching these animes?
P.S. erotic content is fine (appreciated =D) but only as long as it doesnt take precedence over the plot, so dont give me hentai please.

I don't care if its licensed in the usa. I live in europe and I can download whatever I want legally as long as its for personal use.
I love swedish law :)

My advice is....

Azumanga Daioh <<-- slapstick in middle school
Serial Experiments Lain <<-- mindfucker
Kimi Ga Nozomu Eien <<-- Drama (made me (guy) cry, THAT good)
The Melancholy of Haruhi Suzumiya <<-- just good/mindfucker
Rozen Maiden <<-- made me wake up out of my bedroom and actually started going back to school.
Rozen Maiden Traumend <<-- 2e serie of above
Elfen Lied <<-- Serious Action
Haibane Renmei <<-- created by Yoshitoshi ABe (says enough IMO)
Hellsing <<-- Vampiric drama
Kanon <<-- romantic drama
My Hime <<-- Drama, with fantasy and a tip of romance
Princess Mononoke <<-- Adventure drama


Well, there are more but I can't be arsed to copy/paste them :)
ow and look in this site for more information about the anime
http://www.animenewsnetwork.com/encyclopedia/anime.php