tedrlord

If you haven't yet seen Read or Die, you're missing out. It's a really short mini-series (three episodes) but it's quite entertaining.

As for other anime, I'd recommend a lot of what other people are saying. Kare Kano is great, even if shoujo (girl) anime isn't your thing. Hell, Gainax did it, enough said.

GTO (Great Teacher Onizuka) is a really funny series, too. If you like it, I recommend reading the manga, which is even better.

Love Hina is pretty entertaining for a harem-type anime. The animated series is really funny, but seems a little one-dimensional sometimes. The manga, on the other hand, is excellent. Easily my favorite in print.

Someone mentioned Goldenboy, which is also very funny. Though it can get pretty perverse sometimes, it's not a hentai. The really cool thing about it is that it has the same character designer as Cowboy Bebop, and one of the girls looks a hell of a lot like Faye. Oddly enough, despite the fact that it's obviously male-targeted, it's one of my girlfriend's favorite series.

I assume you've seen Evangelion. If you haven't, just go do it now. That's all I have to say.

Since you mentioned Cowboy Bebop, I'll also recommend Noir. It's along a similar vein, though not so sci-fi. It's about a pair of female assassins that mostly just kick ass while trying to figure out who they are and what brought them together. It's a fun show.

Serial Experiments: Lain is a very complex and strange anime. The shining example of the techno-spiritual "mindfuck" genre the Japanese seem to like.

Fruits Basket is a very shoujo series, but I thought it was pretty cute, and my girlfriend totally adores it.

On a related note, I know I'll sound strange for this, but Card Captor Sakura is quite good too. It somehow manages to be very sweet and cute and pleasant while still being interesting and well-made. It's a very large series, but I recommend watching at least a few episodes.

Other than that, I can't think of many more off the top of my head.