This article is from the Final-Fantasy and other Square Soft Games FAQ, by email@example.com (Nick Zitzmann) with numerous contributions by others.
Yes, there are; there's two of them.
"Final Fantasy: Quest for the Crystals" is a Japanese animation that's
set in the world of Final Fantasy V, one hundred years after the death
of ExDeath. It has been translated, and you might be able to find a copy
in some stores, especially ones which specialize in Japanese animation.
"Final Fantasy: The Spirits Within" is a CG movie not based on any of
the previous Final Fantasy games, although the storyline has some
elements in common with Final Fantasy VII's Gaia theory theme, and it
was directed and co-produced by Final Fantasy series creator Hironobu
Sakaguchi. It ran in theaters during summer 2001, and should be
available for rental and purchase (as of 12/31/01) on DVD and VHS.