Another, Stardust (by my favorite author Neil Gaiman) has a great movie adaptation, which is neither worse or better than the book. Most movie adaptations try to do too much, while achieving very little of the actual book. Gaiman helped write the screenplay, so the movie did a great job of leaving out the stuff that didn't matter, and changing things around enough to make it a great film on its own.
This - Stardust - is the one first one that came to mind when I saw the thread title. The book is too much of a downer for a light fantasy and the movie hits it just right.
I also think "The Godfather" was a better picture than Mario Puzo's book.