There's plenty of free software which will do the job but this website offers the simplest way to do the job:
http://keepvid.com/
You should note that Youtube uses Flash video so, when using that site, it's important to ensure that you save your videos with the .flv file extension on the end of the name. You can then burn them to disc in the same way as any other files.
However, you can't play Flash video files with Windows Media Player. You need a better media player, such as VLC or GOM:
http://www.videolan.org/vlc/
http://www.gomlab.com/
If you'd prefer a software-based solution (which allows you to convert the downloaded FLV files to other formats), try this:
http://www.download.com/YouTube-Downloader/300 0-2071_4-10647340.html?tag=contentBody;mostPop TwoColWrap&cdlPid=10801797
Chris