I don’t use Skype very often, but when I went to use it recently, it couldn’t see my FaceTime HD camera.
I’d go into Skype > Preferences and in Audio/Video and although the preferences said it was using the FaceTime HD Camera, the video was black, and my contact at the other end of the call couldn’t see me.
To fix this, I went into Activity Monitor and searched for a process called VDCAssistant. I quit this process (and it respawned straight away) and immediately, Skype could then access my camera.
I’m not sure what caused it to stop working in the first place, but at least the fix was quite easy.