I third the Utena recommendation. Very.Good.Show.Period.
Ghost in the Shell- Very good movie. I have no idea how to describe it other than government intrigue, lots of computers, and a puppetmaster. (I'm bad at summerizing)
Record of Lodoss War OVA- If you like classical fantasy (elves, dwarves, wizards, magic etc) then you should watch this. It follows a young knight-in-training named Parn through his adventures in Lodoss as he struggles to prove himself worthy. After rescuing the king's daughter, everything esclates and he finds himself participating in a huge war against the Marmo (the bad guys), fighting dragons and saving all of Lodoss from destruction. Dragons, fantasy beings and a good storyline, 13 episodes; watch and enjoy.
Heat Guy J- Darn MTV2 for not finishing this series!!! Anyway, Heat Guy J... it's about a boy name Daisuke and his android named J. Together, they combat crime in the city-nation of Judoh. Their biggest advisary is Claire Lionelli, the Vampire (or leader guy... or godfather geesh) of a powerful mafia that manipulates the stock market, tries to blow up the city with high intensity explosives and a bunch more crazy stuff. They end up befriending a werewolf named Boma who is looking for his sister? He appears every now and then but I think he has a bigger role near the end of the series. His attribute, randomly appearing and asking "Have you seen, my bunny?" I wish I could tell you more, but again, MTV2 never finished the series, I only have the first 4 episodes and everything else is fun. But if you find a DVD pick it up and watch. 26 episodes, good animation, lovely music.
Vampire Hunter D: Bloodlust- I feel that if this movie were a TV series, it would be very cool. Anyway, a much improvement over the first VHD movie, Bloodlust once again follows D, a dunpeal (half human half vampire) as he tracks down a man's only daughter, Charlotte, who was seemingly kidnapped by a powerful vampire named Meier Link. To add his troubles, D has to up with competition from the Marcus Brothers, a vampire slaying squad sent on the same rescue mission. As the story progresses, we find out Charlotte wasn't kidnapped and in actuality is running away with her vampire love to escape the world where vampires are feared and hated. Meier had implored the help of another vampire, Queen Carmella, to arrange for a ship to take them to the City of the Night but all is not as it seems. In the end, D catches up to Meier and the final battle for love insues. Mystery, romance, action, a bit of angst, pretty animation and nice music. Great movie.
Cromartie High School- There is no way I could describe this fully. This is just something you have to see to believe. Basically, a bunch of delinquents at Japan's baddest high school; are they really has bad as they seem? Nope. Basically, just a bunch of teens dealing with life in a not so normal fashion. The series is hilarious and very addictive. Currently running on Anime Network OnDemand for any Comcast folks out there.
I have a ton more but I don't think I can think up summaries for them all so I'll just list them.
Rurouni Kenshin, RahXephon, The Vision of Escaflowne, Neon Genesis Evangelion, Cowboy Bebop, X/1999 TV, Sailor Moon, Trigun, Hamtaro (yes, Hamtaro. Gotta love the cute stuff), Fishigi Yuugi, Mobile Suit Gundam 0079, Gundam Wing, Tenchi Muyo OVA and Tenchi Universe, Armitage III, InuYasha, Last Exile, and Yami no Matsuei (Descendents of Darkness).