I add my vote for
Record of Lodoss War. It's very satisfying for fantasy fans, I think, whether you play D&D or not. Be advised that there are actually two series of this, and the second series somewhat repeats what is in the first.
I also enjoy
Inu-Yasha and
Slayers. I haven't seen much of
El-Hazard, but what I have seen I liked, and the same goes for
Escaflowne.
If you're interested in something short and humorous, try
Those Who Hunt Elves. Don't worry if you like elves; they're not hunting them to kill them.
For great anime fantasy that isn't a series, try
Princess Mononoke and
Spirited Away. These are some of the best there is.
Nausicaa of the Valley of Wind is another good one; it may appear under a different title in some places, but I don't remember what the stupid American title is. Anyone want to help me out here?
I'd also recommend something that isn't technically anime (it's not made in Japan) but is done in a very anime style, and has a great fantasy story:
Avatar - The Last Air Bender, on Nickelodeon.