This is a problem with Firefox 3.6.14. Update to the latest version, pronto. (Firefox 3.6.15) The easiest way is via the Help menu. Help>Check for Updates.

Thanks. I took you advice, but it's still not working.

If I use the old Adobe plug-ins, the "out-of-date" ones, I have no trouble with Youtube and videos in general. A yellow bar appears more or less constantly warning me that my plug-ins are out of date. Tired of seeing it, I installed the latest ones again only to find that the problem re-appeared. When I reverted to the out-of-date ones, I could play videos and use Youtube.