Ok the first anime set you will want to get is Neon Genesis Evangelion. It is still one of my favorite animes of all time.
Next are a couple that I really likes that I think are licensed.
.Hack//Sign -- An anime about a MMORPG
Scryed -- I don't know if this is licensed but it is an awesome anime.
Since anime is so costly to get on DVD I will stop there.
Just a couple words of advice.
One -- Watch it with subtitles if at all possible. The japanese voice actors are almost always better than the american ones. The animation is also matched to their voices.
Two -- If you have a fast internet connection then you can download anime that has not been licensed yet. If you want a good place to get subtitled, unlicensed anime go to
www.animesuki.com
Three -- If you don't like one series then try another. There are a lot of different types of anime out there.
Hope some of this has helped. If you want any more suggestions then just ask again
