My suggestions would be the following (in no particular order), some of which are easier to find than others:
Ninja Scroll - Decent story, great animation.
Dagger of Kamui - Good story, good animation, long feature.
Record of Lodoss War - Fun story, good animation. If you ever liked Dungeons & Dragons, you'll like this.
Ranma 1/2 - A funny comedy series. It's one of the best of the sillier animes.
Vampire Hunter D - A good gothic horror type anime. Good animation, good story.
Escaflowne - Cool story, good animation.
Dominion: Tank Police - It's got really cool cat chicks for bad guys. What more could you ask for?
Oh! My Goddess! - One of the most amusing out there. Well worth watching.
Princess Mononoke - One of the greatest Anime's ever. Currently the second highest grossing movie of all time in Japan (after Titanic). And well deserving of it's place, as it's one of the best I've ever seen. Created by Hayao Miyazaki, the best guy in Anime, period.
Nausicaa of the Valley of Wind - My all time favorite Anime. Absolutely amazing. Everything about it is just impressive. Very difficult to find. Never watch the English dub/hack, called Warriors of the Wind. In the edit, they cut around half an hour, half the plot, to make it more action for kids. Totally ruined it. Another one by Hayao Miyazaki, considered by many (including me) to be his masterpiece.
Hrm, there's a lot of others I like, but I can't think of them off the top of my head right now.