If this happens to you, there are several things you can do.
First you can check out http://teachertube.com/, which is the YouTube for teachers, but there aren't as many good videos to choose from. It's a great idea, but it needs more users to put up some better content. There are a few organizations who have taken to it, and posted some good historical content, but it might be a struggle to find exactly what you're looking for.
And finally you can use Zamzar (http://zamzar.com/) Zamzar is a file conversion website that can convert almost any type of file to the format you desire. In this case, you can input the URL of the YouTube video you desire and convert it into a format that you can save to your computer or your zip disk/thumb drive and access directly from your computer. Sometimes the files are rather large so I don't recommend emailing it, but you can certainly email the URLs of the videos and convert them from your school's computer.
Zamzar is quite simple. Just have it sent to your school email address and save it there. Hopefully you have a network, because the files are quite large, and it would be easier to share with other teachers.