I consider the magic that takes place in The Lord of the Rings to be very unique. In many of the current crop of fantasy stories, a human finds out that he or she has a special gift that is construed as magic. He or she uses this newly-found gift to solve some problem, and there is your story.
The magic in The Lord of the Rings is interesting to me because, even if magic might be used for the occasional good intention, it actually causes more problems than it solves. Furthermore, none of the beings performing magic are human, or even mortal.