Are you inside a school or other organization, or do you use a proxy?
At my school, there is a content filter/proxy (which I'm pretty sure has some glaring bugs...) that requires login with student ID / password. Some globally unblocked websites (such as youtube) will load, but the domains the videos are hosted on are unblocked when logged in. If you're not logged in to the filter, no video works, period. Issues similar to this are common with this particular proxy...
Bottom line: I see this issue often if you can access youtube.com, but you can't access the other related domains that youtube stores the actual videos on.