Akira, definitely. That is the most important Anime movie you could watch, in my opinion. There are two versions - the classic, and the remake. The classic has the original animation, and is great, but not of the best image quality. The remake is the same art, but completely redone animation, so it looks much better and smoother. The remake also has a completely different translation from the Japanese version, and different voice actors. There is not a better one out of the two, except maybe the remake has more straight forward lines, and maybe easier to understand for some people. Whichever version you watch first will hurt the other version. By which I mean you're used to the movie sounding a certain way. I suggest you watch the classic first, because it is the classic.
The Street Fighter movies, if you're interesting in action Animes. Fist of the North Star is pretty good, too.
Full Metal Alchemist is something you should definitely watch! But it's not too dark.
If you haven't seen the second Vampire Hunter D movie, "Bloodlust" then you should watch that. I'd say it's okay.
Twilight of the Dark Master is okay, but it's only about 45 minutes long and doesn't have a great storyline.
Wicked City is good, which is a lot like Twilight of the Dark Master, except with better voice acting, better characters and better storyline. Regular length, too.
The Cyberpunk collection, if you can find it. I've never seen it before, myself.
Grave of the Fireflies, is a very deep and interesting Anime about the Hiroshima bombings in Japan.
Legend of the Overfiend. It borders on Hentai, but has an amazing story, and excellent art.
If you're going to watch Anime, you might as well read Manga, too. Tokypop translates a bunch of Manga. Battle Royale is definitely Manga you should read.
