A few days ago, I learned I couldn't play YouTube videos in Safari 6. Every YouTube page displayed a black video window with no player controls. Firefox and Chrome were working fine so it wasn't a YouTube issue. I then learned that our iPads were having the exact same issue.
After posting a question on the Safari forum, a helpful soul gave me the solution. It turns out that Google automatically signed me up for the HTML5 beta. The fix is to go to YouTube HTML5 Video Player page and click the link at the bottom of the page to remove yourself from the beta.
Shame on Google for automatically enrolling people in a beta program for something that doesn't work without telling the user what they've done.