I've had a hard time when I tried to save a youtube video. The easiest way to do it without compromising the security of your machine with the countless plugins and add-ons is to

1. clear your cache
2. load the youtube page with your video
3. explore the cache to find the cache file (it should be the biggest in size)
4. copy the file to another directory
5. rename the file and add the extension .flv

That's it.