The other day I posted about the Cosmopod plug-in for Safari that allowed you to easily download and convert embedded video files in a web page. There is a similar solution for Firefox although the video files are downloaded as is, for example, .flv files. It is a Firefox add-on called Download Helper. It will allow you to easily download video files from YouTube.
Now, if you would like to view the files using Quicktime Player I suggest that you download and install the Perian Quicktime plug-in. As their opening screen states… “Perian is a free, open source QuickTime component that adds native support for many popular video formats”.