Ooh, I like a bunch of your likes.
Vision of Escaflowne: A young girl from Japan crosses over into a fantasy world with low-tech mecha. Oldie but goodie. Pretty animation, especially for the time period, and phenomenal soundtrack. 26 episodes. The movie is a retelling of the series and isn't nearly as good, IMO.
Noein: Lovely little coming of age story mixed with quantum physics-based time travel. 24 episodes.
Eden of the East: Short and quirky and almost impossible to describe, but I loved it. (I guess it might fall into SF?) I think it was 13 episodes + two followup movies.
Samurai 7: Steampunk remix of the Kurosawa movie. Same studio as Last Exile, Hellsing, and Gankutsuou. I think 26 episodes.
Wolf's Rain: In a dying world, four wolves (that can pass themselves off as humans) search for Paradise. 30 episodes, but there are 4 filler eps in the middle that you can safely skip.
Darker Than Black: Weird and spooky, gorgeous animation, first season is 26 episodes. Present-day... urban fantasy, I guess? With spies and people with strange powers. There is a second season that I did still like but isn't as good, IMO.
Paranoia Agent: 13 episode series by Satoshi Kon, who directed Tokyo Godfathers, Perfect Blue, and a number of other acclaimed anime films. Defintely surreal, but I didn't find it confusing.
Recently finished and enjoyed Princess Tutu, a sort of metafictional ballet fairy tale, but might be too romance-oriented and/or silly? 26 episodes.
This is just a standalone film, but I thought Summer Wars was really funny and uplifting. (The world is threatened with destruction through the power of the Internet! The world is saved... through the power of the Internet!)