I actually have a list from this review site thing, that I really want to watch, but I can't seem to get my hands on any of them. American animes just don't stand up to the true Japanese stuff...
Toaru Majutsu no Index is some weird... not really magic, but people have powers, in this city, the academy is a place where you can get powers through science. These people are called espers. This one level 0 esper (the lowest level) meets this one girl that says she can do real magic, not scientific magic. Btw, the level 0 esper can cancel any esper ability with his right hand... thats what makes him the main character :D
Akikan- forget
Kannagi- forget
Tales of symphonia- some kinda medieval thing if i recall
World descruction - Well, this is pretty interesting... hard to explain though, i saw only a little of it
Even no jikan, or time of eve - about humans and androids, the androids normally do all their masters requests. 2 kids walk into a cafe, where there is no discrimination between humans and androids, therefore the androids get personalities, and androids lose their ring, which is what makes them look different from humans.

.. this one i want to watch the most, because it is reall short, and i should be able to watch it in a weekend or 2... 6 episodes i think