Symptoms: flash works but YouTube videos not load.
You probably use some ad blocker like AdBlock for Firefox or AdSweep for Chromium. If you are – they are your problem. Unfortunately only solution I have already found is to disable that extensions. YouTube will just start working again.
Hope it helps.
Solution found here: http://www.linuxforums.org/forum/redhat-fedora-linux-help/103254-youtube-not-working-fedora-7-a.html#post507361
Update:
For Firefox you can try this: http://kb.mozillazine.org/Flash#Adblock_conflict