Different sites have different ways of showing videos. Sometimes they put a lot of effort into keeping you from downloading the video files to your hard drive and sometimes they don't mind and make it easy.
Whitehouse.gov makes it easy. Look at the html code for the page that opens when you play the Quicktime Barney video, for example. There's a link to:
http://mfile.akamai.com/5913/mov/whitehouse.download.akamai.com/5913/barneycam/barneycam2008.mov
If you right click on this link:
BarneyCam you can do a 'save target as' or 'save link as' and save the file to your computer.