I would suggest you to try installing Google Chrome, but it could be useful to know what Operating System you're running (Windows Xp/Vista/7, Gnu/Linux of what flavour, MacOS 9.2/X, etc ?)
Best regards
EDIT: while you're waiting for some REAL solution, you could be interested in this: http://www.kissyoutube.com/ When you are watching a video with the behaviour you've reported in your answer, add "kiss" to the URL