Do you know if any of your readers have had the same problem? If not, it may be that it’s a local problem and that what you need to do is to update Flash. Youtube only works properly when Flash is up to date.
It could also be that you need to clear your browser’s cache and try again.
It might be helpful if you could upload a youtube video to one of your posts so that we can try it – then if it doesn’t work for us, it will rule out a browser issue. (You could put it in a backdated post if you like, and delete it later, that way it won’t look out of place to your readers.)