If you want to cache/copy youtube videos for later use, go tor you firefox cache and just copy the flv files over.
My Name\Local Settings\Application Data\Mozilla\Firefox\Profiles\rxxs25wm.default\Cache
The filenames are like:
Add .flv as your file extension and then open a valid flv player.
Look for the files that are over 2mbs. And normally you have to watch a complete youtube video, wait until it caches and then close firefox for the cache to be saved to disk.
And another note, I watch a lot of youtube videos. Every youtube download may cost you 15mbs of bandwidth. So I would consider watching the videos from file.
I ate up 20gigs of bandwidth last month. I think my isp is considering charging me extra.