A lot of the stuff I would recommend has been mentioned so I'm going to list a few older goodies.

Battle Athletes (Preferably the TV series, cause it has the better cast and story) Now I generally don't care for sports anime but this one is hilarious and touching.

Irresponsible Captain Tylor the funniest anime ever! Only show where a captain defeats an entire fleet of aliens just by surrending at the right time

One Pound Gospel, the story of a boxer who falls in love with a nun. It's Rumiko Takakshi but it's more in the vein of Maison Ikkoku than Inu-Yasha or Ranma 1/2

Robot Carnival, it's pretty old and hard to come by but it is gorgeous and entertaining. If you like to see how diverse anime is, this movie is the one to do it. It's a series of animated shorts done by famous directors and writers in Japan arounf the mid 80's. They all share the theme of robots. At times it's funny, action packed, artistic and somtimes just plain beautiful... It's a real hidden gem of an anime.

Captain Herlock: anything with Harlock in the title. In fact, anything by Leiji Matsumoto.

Slayers, cause it's the best damn fantasy anime made. The karaoke scene in season two is alone worth watching this series.

Tenchi Muyo! preferably the OVA and the first movie. Their funny, action packed and surprisingly touching and heart warming. The first movie is gorgeous and has one of the best Tenchi stories.

I'll see if I can remember anymore later.