The Twelve Kingdoms
I think this has become my favorite fantasy anime in quite some time. Certainly it excels in world-building, characterization, plotting, and high quality art.
The first five episodes are gritty, depressing, and angst-ridden...but there's a very good reason for all the emotional and physical upheaval the protagonist goes through. It was refreshing to see a Japanese high school student end up in a mythic version of ancient Asia and not end up knee-deep in bishonen.
Plus, it has kirin and a kindly rat among the lead characters. What's not to like? ;)
Seek it out, but be wary...the first five episodes are good, but don't make for cheery viewing. And a lot of the mysteries and growth from the character seeds planted in those episodes don't unfold until later. Since the series is based on a novel, think of every few episodes as roughly equivalent to a "chapter".