You can download a program for your Mac or Windows computer dedicated to downloading web videos. For Mac, see MacTubes. Windows users can try Free YouTube Downloader. Both softwares have received solid reviews and work as advertised.
This Firefox browser plugin also works with many popular video sites, including Facebook. Once you install the extension from the plugins site, a button will be added to your toolbar.
To use it, go to a page with embedded video. You will notice that the NetVideoHunter button will blink and let you know that the video can be downloaded from the page. Click the button and click Download next to the video you want to save.