Who is speaking in the prologue to the film?

It is Galadriel (Cate Blanchett) who narrates the prologue. It was originally going to be Frodo, but it was felt that this would give too much of the story away (i.e. that Frodo makes it through his perilous journey with the ring). There was also one version with Gandalf, but that would have resulted in similar problems involving giving away later events. In the end, Galadriel was chosen due to her ageless quality and her all-knowing actions in the film.