Sothink Web Video Downloader for Firefox is your solution. Its free, and its extremely easy to use.

Just install the extension to your Firefox. When you are playing a web video in youtube for example, they will prompt you whether you want to download the video. Click yes, and it will start downloading.

You can even convert the video to other formats (default is flv).

Get the extension here!
http://www.sothinkmedia.com/web-video-downloader-firefox/download.htm