There is a plain and easy way to download YouTube .flv videos (which you can watch with VLC Media Player, or in a Mac with Quicktime Player and additional plug-ins).
To do so, you need the Safari Web Browser (Mac or Windows). Go to your desired page hosting a Flash Video file, and select Activity in the Window menu. There you will find the files being downloaded in the web-page you are visiting… double click the bigger one (as usually flash videos are the biggest files in YouTube pages, if you can’t find such a big file, check for the .flv file extension) and it will open in a new window. Just save this file and you are done :)