Any guesswork?
Movie|Line thinks it'll be Apichatpong Weerasethakul's
Uncle Boonmee Who Can Recall His Past Lives but allows for
Another Year, Biutiful or
Un Homme Qui Crie (
A Screaming Man) as spoilers. While most cinephiles would be happy with Weerasethakul winning something as major as the Palme D'Or but I've found in the past that predicting the winner based on what we know of the jury president's aesthetic -- in this case Tim Burton's -- is not always the best way to go. Burton and team (there are other people voting after all) could hand their prizes to virtually anything. We'll see.
Update You might be able to watch the closing ceremonies
streaming here at around 1:00-1:15 pm EST time.