Reminds me of the famous short story by Arthur C. Clarke, "The Nine Billion Names of God"
http://lucis.net/stuff/clarke/9billion_clarke.html
Not exactly the same argument of course and that was with monks instead of monkeys. They also sort of cheated by using a computer to find all possible combinations of nine letters. In the story it was estimated that if done by hand, it would take the monks 15,000 years (not sure how accurate that is - I think it would take a lot less time but hey, it's a fictional story).
Nine letters isn't quite the complete works of Shakespeare, LOL.
As another poster said, I think eventually all of the words would occur but likely not in the same order. Then again, infinity is infinity so anything could happen.