If you come across a clip that has only audio and no video (just a black screen after the clip starts playing), click on the full screen view. It should show the video image again so you can then return to standard size and it will continue playing with both audio and video. Most people have no problem watching videos on YouTube itself and it seems to be an issue only with embedded clips on other sites.
My hunch is that this was caused by an update to the YouTube API to prevent automatic video downloaders that also possibly conflicted with an update to the Flash player. Although it doesn’t seem to happen with all embedded videos.
I’ve been having this problem for quite a while with clips on my blog, and while I haven’t found a permanent fix for it, this should allow you to view embedded videos without too much inconvenience.