Josh Kinberg of sandbox films was kind enough to share his programming expertise in creating Greasemonkey scripts that allows you to save local files of both YouTube and Google video files. Check out his blog post here for the scripts and more information on how they work.

Both of these scripts will allow you to save the videos as Flash .flv files (you may need to supply the extension). If you don't have a means to play such files (I didn't), then you can download an FLV player from download.com.

For those of you unfamiliar with Greasemonkey, it is a Mozilla Firefox extension that allows users to write scripts to change how you interact with specific web sites, usually adding or supplementing the page content or changing its design or function. If there's enough interest, I'd be happy to make a more detailed post with some of the scripts I use regularly.

Enjoy!