There are many programs and services that provide this, the one that I use often is from Voobys.com
It works like this:
- go on YouTube to the video that you want to download
- change in the address bar of your webbrowser youtube.com for voobys.com
So for example:
http://www.youtube.com/watch?v=VL72OBcgc9U
becomes
http://www.voobys.com/watch?v=VL72OBcgc9U
and that's it, then you can download the video in .flv format, which you can play with for example VLC Media Player
