YouTube relies on Flash Player working properly. It has a nasty habit of packing up for no apparent reason.
Uninstall Flash Player. (With XP, and earlier versions of Windows, go to the Control Panel and double-click on Add/Remove Programs. Uninstall 'Adobe Flash Player plugin'. With Vista, other than in Classic View, go to the Control Panel and, under Programs, click on 'Uninstall a program'. In Classic View go, via the Control Panel, to Programs & Features).
Then reinstall Flash Player from here:
http://get.adobe.com/flashplayer/
Chris