My computer had this problem. YouTube videos are just a black box. I tried reinstalling Flash Player but it didn't help, you just have to uninstall FireFox and then reinstall it again. If after reinstallation it still doesn't work clear all of your cookies.
I came here to start a thread on this, so thanks for saving me the trouble. I've tried reinstalling Flash player, fiddling about with Adblock Plus and clearing cookies, but no good. I don't want to reinstall Firefox unless I absolutely have to - it takes me ages to get it all pretty again afterwards.... I don't want to give up FF because I am pathetically devoted to Colourful Tabs... I assume it's related to some kind of upgrade, since it's happening to a lot of people. Is it worth just sitting it out and waiting for them to fix it? (I'm not very technical.)