Well that's certainly odd. If you'd said that the problem related to all sounds I would have suggested reinstalling the sound driver. If you'd said that it affected all streamed videos I'd have suggested uninstalling and reinstalling Flash Player ('cos that's what Youtube and other video-streaming sites use to display video content).
Are you sure that you've not accidentally clicked on the Mute button on a Youtube page? (It's the one with a speaker symbol on it, next to the Play button).
Otherwise it might still be worth uninstalling Adobe Flash Player Plug-in (from Control Panel > Programs & Features) and then reinstalling it from here:
http://get.adobe.com/flashplayer/
That's among the suggestions here:
http://support.google.com/youtube/bin/answer.py?hl=en&answer=58132
Chris