[SLTE]

Cowboy Bebop and Trigun are two awesome ones, and they're not very long. I'd also say Samurai Champloo and Seven Samurai if you like anime that are a little closer to Japanese culture.

Did you watch both versions of Fullmetal Alchemist, or just one or the other? I'm surprised to say that I like both of them pretty evenly, even though the story veers pretty wildly in different directions depending on the version. Brotherhood probably wins by a nose, but the 2003 version is still very much watchable and enjoyable.

[oahuwriter]

I only saw Brotherhood. When the two Elric brothers finally saw their father and when they got their bodies back is the part I like the best. Some of the episodes are so sad, but as a whole I like Full Metal Alchemist too! I like Cowboy Begop and Samurai Champloo. I did not see Seven Samurai or Trigun yet.

[Elfprincess]

OP mentioned enjoying GITS, so I would like to recommend the short series (or a movie) Eve no Jikan.
It touches on what it means to be a human, and the issue of artificial inteligence. In the series, androids and gynoids are serving humans. They're identified by a head accesory that they're forced to wear.
There's a cafe in which androids can take it off, so no-one knows who's human and who's not.
It's an extremely well-done anime with interesting concept - shame that most people never heard about it.