Jaksta is by far the best/easiest/painless solution I've seen for saving Youtube, Vimeo, or almost any other streaming video or audio content. It's definitely just become what I would consider an essential production tool.
You can check it out here: Jaksta Streaming Video Capture
Just a tip, I don't recommend leaving this thing running and forgetting about it or you'll accidentally download practically everything & end up with a ton of stuff you don't want/need. Better to just load it up when you need to grab something then close it down completely.
Jaksta is $49.95, so it might be a little overkill for general use, but will totally pay for itself in time saved if you often find yourself needed to source content & clips for presentations, pitches, meetings, or any number of other particular situations you might find yourself in while in production on something.