Personally, I would steer clear of directly promoting the use of any questionable knowingly illegal downloading methods on these forums. While I'm pretty indifferent towards the use of such sites as thepiratebay.org or such programs as uTorrent, it should perhaps be pointed out to some of the newer people in SK that controversies have arisen from the illegal and/or perceived illegal use of the Internets here. I've also heard of US companies going after people abroad. I know this site is supposed to be 'safe' but, really, what is safe on the Net these days??
That said, savevid.com is a great website that you can use to legally download videos from various websites. It works great with YouTube allowing you to choose from several different file formats, some already Ipod ready. It's been a big help for me at school, too. If the internet isn't working in your classroom, or if it's just really slow, and you wanted access to some video on the web then you could use savevid.com to download the video on another computer (with internet of course!) and save it to a USB.
Also, if you're tech savvy enough it's fairly simple to strip the audio from those videos and convert them to another format if necessary..