Stand By Me and Shawshank Redemption are good examples of the adaptation being an improvement. Then again, adaptations are usually a novel being adapted for a shorter telling rather than a short story being elaborated.
Those are great, but The Godfather is my favorite example. The book is, honestly, terrible. The prose is bad. It focuses almost exclusively on the salacious - does it need to tell us that many times about the size of Sonny's cock? - and enjoys the violence a bit too much. None of the minor characters leave any impression at all. The movie, though, is... The Godfather. It transcends it's source, without transposing or changing anything - in fact, I suspect it's far more faithful to its historical setting than the novel - more fully than any adaptation I'm aware of.
Those are great, but The Godfather is my favorite example. The book is, honestly, terrible. The prose is bad. It focuses almost exclusively on the salacious - does it need to tell us that many times about the size of Sonny's cock? - and enjoys the violence a bit too much. None of the minor characters leave any impression at all. The movie, though, is... The Godfather. It transcends it's source, without transposing or changing anything - in fact, I suspect it's far more faithful to its historical setting than the novel - more fully than any adaptation I'm aware of.