So
Rem, you are looking for suggestions that "Fit the mold" so to speak? Hmm...
Anime - Sci-FiChobits - I still think of this anime as one of my favorites. It is also one of the best for "android" style sci-fi.
Eve no Jikan - If you aren't using Chobits then this is "The show" for androids. Very Asimov. An anme that makes you question, "What defines a human?".
Starship Operators - Not very popular, but probably the most
Star Trek like anime out there. Did Roddenberry write this show?
Planetes - This one is in the not so distant future. Not so far fetched as most anime.
Anime - FantasySlayers - Pretty self explanitory, this show is the epitome of fantasy.
Kemono no Souja Erin - By the same author as
Seirei no Moribito. I think both are worthy of best fantasy anime.
The 12 Kingdoms - Another popular fantasy anime.
Tears to Tiara - Is an anime that almost tries to hard to be fantasy. It goes to extremes to have everything.
![Roll Eyes ::)](https://www.kumoricon.org/forums/Smileys/default/rolleyes.gif)
You wont have time to talk about or show every anime there is, but I think these are pretty fair representations. I didn't go into the entire spectrum of Mecha anime, or the space battle anime, there are so many, and everyone has their favorites. Macross and Gundam, Captain Harlock, Voltron, Zoids, the list goes on and on. There is also the entire "Magical Girl" series of anime. These can be classified as fantasy. How you want to classify vampires and aliens is up to you. Plenty of anime about both.