Answers in this forum have shown different things have worked for different people.

For some clearing YouTube cookies and the cache solved the problem. For details of how to do that see https://support.mozilla.com/kb/Deleting+cookies and https://support.mozilla.com/kb/How+to+clear+the+cache

Others had to go a step further after deleting YouTube cookies and block YouTube from saving cookies. In the Tools menu select Options to open the Options window. Go to the Privacy panel and make sure it is set to "Use custom setting for history". Click the Exceptions button, type in http://www.youtube.com and click on Block

Another option is to disable hardware acceleration for Flash. To do that right-click on a Flash video, select Settings, go to the first tab of the settings for the option to enable/disable hardware acceleration for Flash. This is something recommended by YouTube for those having problems - http://www.google.com/support/youtube/bin/answer.py?&answer=1209379

I've done all this AND updated to 3.6.16 and it's still not working.

It was working earlier in the week and 3.6.15 broke it.

Mac OS X 10.5.8 on a G5 PPC Mac. Flash 10.1.102.64 ( the latest version for PPC that I know of.)