Jason wrote up a great post over at Hackszine on how to download Youtube and Google videos using Safari or Firefox:

There are a few different ways to get at the FLV file that the video player application is downloading. Safari users can use the Window->Activities feature to locate and download flv files as they are playing, and Joshua Kinberg put together a couple nice Greasemonkey scripts for Firefox that make downloading pretty simple.

I was looking for an easy solution that works cross-browser, and this is what's working for me: 2 javascript URLs, based on the original code from Joshua's Greasemonkey scripts, that you can add to your bookmarks list.

Google Video Download Bookmark (right-click, copy address and save to bookmarks)
Download Google Video

Youtube Download Bookmark (right-click, copy address and save to bookmarks)
Download Youtube Video

Don't click on those URLs here. Just get them into your browser's bookmarks. The next time you are watching a video on Google Video or Youtube, you can click the appropriate bookmark and a window will pop up that will begin downloading the FLV! The Youtube file will be named "get_video" after it is downloaded. Just rename it and add a ".flv" extension and you should be in good shape.

You can read the full post here and read related articles.