The Lord of the Rings novel was not considered a trilogy until Peter Jackson came in and made the movies. In essence, the Lord of the Rings novel is in fact a remake, a retelling if you will, because:
1) Tolkien considered himself a "translator" of the Redbook of Westmarch, which is the fantastical book written by Bilbo and then Frodo and then to Samwise and on down. From the came "There and Back Again (the Hobbit)" and the Lord of the Rings.
2) Tolkien was heavily influenced by Celtic and Germanic mythology and languages. Some of the same elements, he drew upon to write his fictious stories about Middle Earth.
I greatly enjoyed the movies for what they were, the greatest made in that genre and the sheer magnitude of the production, but was left with a yearning to see more. I was so dissappointed that Jackson did not include the "Scouring of the Shire", which tells of the final fate of Saruman, Grima, and how the Hobbits react in a pinch. Oh well...
I'm looking forward to a remake of the Hobbit and hope it sticks a little closer to Tolkien's original story.