My personal recommendations (region 1 commercial releases - gotta stick to what I know):
Slayers, Slayers Next and Slayers Try - Fun, funny fantasy series. Excellent stuff and cheap cheap cheap here in the States. The OAVs and movies don't feature the TV cast and a lot of people who love the TV hate them. Personally I like them but prefer the TV series. On a side note, Slayers and Slayers Next are $44.95 and Slayers Try is $19.95 at rightstuf.com for those in the US. Bargain!
Martian Successor Nadesico - Excellent sci-fi, giant robot, space war series. Has both its funny and serious moments and is well written and very nicely animated.
Excel Saga - Insane. Best word to describe it. It is utterly insane. Probably an acquired taste, though, so check out a friend's copy or dl some on the sly to try it out first. And the va for Excel in the US dub makes my ears bleed, so watch out for her.
Dragon Ball - No Z, no GT, just plain ordinary Dragon Ball. Excellence defined.
Trigun - Funny, action-packed, emotional, full of great characters - this is one of those series that I just go back and watch over and over again. The art and animation are great and the story is pretty decent as well.
Series worth watching that I've seen but don't consider to be 'required viewing':
Scrapped Princess (almost required), Noir, Hellsing, Hyper Police, Witch Hunter Robin, .hack//SIGN, Ranma 1/2, R.O.D. TV
OVAs/Movies worth checking out:
Akira, Read or Die, Ghost in the Shell, Jin-Roh, Perfect Blue, Dragon Half, Ninja Scroll
That's all I can think of off the top of my head. I'm sure I'm missing a lot.