I have seen only a handful of anime movies, but of the ones I have seen, Castle in the Sky is my current favorite, followed closely by the original Ghost in the Shell movie.
The first is a constant inspiration for all of my role-playing concepts, including flying cities, ships of strange design that fly regardless, and pirates who are still human enough to do the right thing.
The second is what it is: a fantastic view of the future, complete with cybernetic upgrades, an uncommon concept of the soul, and the anime introduction of what may be one of the most effective female leading roles ever portrayed (and I really like the color purple).