One of my friends at UHACC pointed me to a neat Firefox plugin called UnPlug. It scans web pages for embedded video content and allows you to save the content files locally. Like if you wanted to download something from YouTube so that you could play it from your hard drive, this tool would do that.
One thing you have to remember is that it must be invoked explicitly. It doesn't change anything in your normal browsing. It must be invoked either from Firefox's "Tools" menu or from the little icon that appears: