This might seem trivial, but once you start an upload of a video to YouTube from your iPhone, I couldn't find a way to cancel it.
Well no more are terrible drunken videos going to get uploaded! Oh wait, yes they will. Nevermind.
Anyway. The simple way? Just set your phone to airplane mode. It turns off the radio, so if you are uploading on your cellular network, this will cause the upload to fail. If you are on Wifi, I would also assume that you could just turn off Wifi and it would fail. If it doesn't, just turn off the radio by switching to airplane mode in your settings.
In Soviet Russia, YouTube uploads you!