Many schools block YouTube. I understand why. While you can find all sorts of great videos, you can also find very inappropriate things. But have no fear–you can use many tools to download those videos. First and foremost–check the Copyright on the videos. Many are released under Creative Commons, but many are still subject to Copyright, so please make sure you check that!
Recently, the Lifehacker blog shared DownloadTube (http://lifehacker.com/5667809/downloadtube-is-a-one+click-youtube-conversion-and-download-site?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed:+lifehacker/full+(Lifehacker)). While at first glance, it looks GREAT, one gaping problem is it leaves a huge watermark on the video. Epic fail! I use a great site, Media Converter (http://www.mediaconverter.org/). You can create an account, but you can also download individual videos on the fly, without an logon.
The interface is pretty easy. You take the YouTube link, put it in the box, and in a few minutes, you download the video from a link. Easy! Pretty good quality videos as well.