This isn't exactly the easiest thing to accomplish if you're not using Firefox. So, get Firefox. Download the Download Helper add-on. That's it. Once you have this installed, you'll have an icon on your toolbar.

Navigate to a web page that has YouTube videos on it, then click the drop-down and you'll see a list of the YouTube vids on that page and you can download them to your computer.

Now that you've got the FLV file saved to your computer, you'll need something to play it. It's doesn't get any better than VLC. Download, install and you're on your way.

If you're using IE, then you'll need a separate program to download the files. Look here for a good list to get started. You can also try SaveYouTube.com, but I have found that it doesn't work all the time.