For me it almost always seems to be the one I encounter first. A few films that I consider superior to the book that they are based on include: The Exorcist, 2001, Jaws and The Shinning.
Lord of the Rings is a difficult one for me. Loved the books when I read them years ago, but also loved the films. If nothing else, the films captured how I visualised Middle Earth in my minds eye.
My husband's youngest nephew, Leif Enger, had a best-seller a few years back that is being made into a movie. Brad Pitt is producing it and Billy Bob Thornton is one of the characters. Interesting bit of trivia there! He has just come out with another book as has his older brother Lin. But don't know if they will make it to the top like "Peace Like a River" did.