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.

>>5
Well, Evangelion is basically schoolkid(targeted to angsty teenagers) show AND boring. End of Evangelion as movie is interesting and cetainly not boring, but we have to look the series as whole. Just another mecha-anime, but this time it's pseudo-artsy, better than Gundam or shit like that for sure, but not much better.