I'll assume you mean 'fantasy' as in Lord of the Rings-type swords and sorcery, rather than just general 'fantasy' (which most anime would fit in).
Twelve Kingdoms is probably the best 'Swords n' sorcery' type of fantasy anime I've seen. The story, the setting and the 'rules' of the world are all incredibly well fleshed out. The only problem (besides how annoying the main character is at the start) is that when it ends, you feel there is so much more to the story, even though they do wrap up the main story of the show. There are reasons for that which I won't get into now, but definitely check it out for one of the best Fantasy anime out there.
Scrapped Princess is also high in my fantasy rankings. It's a little newer than 12 Kingdoms and has a real ending, but the overall story is not as rich as 12 Kingdoms is. Escaflowne is great. In fact some of the influential people behind Scrapped Princess made Escaflowne beforehand.
There are lots more, but why bother with lesser shows when you can start with the best. 12 Kingdoms, Scrapped Princess, Escaflowne, and maybe even Lodoss War for history's sake is what you should start with, all in the 'swords n' sorcery' category. All of these are currently available in full on US DVD.
For something brand new, 'Seirei no Moribito' (guardian of the sacred spirit) just finished airing in Japan, and it is another excellent story. The feel is somewhat similar to 12 Kingdoms (rather than Lodoss or Escaflowne) though it's quite a different story. It's animated by Production I.G., most famous for the Ghost in the Shell series, so the animation particularly in the combat scenes is excellent. The artistry in the show is beautiful, the music is probably the best thing to come out of Kenji Kawai for some time, and the story (while it lulls in the middle a bit for extra character development) is smooth and engaging. Highly reccommended.
It was licensed by Geneon before it even started airing, but...Geneon has kind of sunk.