Let's get little
technical here
All video clips played on your internet browser are actually recorded on your harddisk - provided that you enable (browseing History).
For MS Win XP, The "Temporary Internet Files" is a hidden folder in your user folder under "Documents and Settings" and it contains all files, images and clips visited or played on your browser - depending on the no. of days you've set up in the Internet Options tool.
Youtube clips are usually saved in that folder as *.flv files. these flv files are playable - off line- by Rea, Quick Time and few other programs - you may search the net for "FLV Player" - I personally use WinAmp.
The hustle is in locating those files inside the jungle
of "Temporary Internet Files" , copying them to a new folder under different, friendly names.