Many educators (myself included) have enjoyed using www.zamzar.com to download and convert YouTube videos for our classes. It was easy, reliable and it didn’t matter what browser or platform you were using. In other words, it was a great way for teachers to get a hold of YouTube videos for offline viewing. Well kiss that service good-bye. YouTube has officially asked Zamzar to stop allowing people to download YouTube videos as it violates YouTube’s terms of service and so on. This is by no means killing Zamzar. They still offer the ability to upload and convert files online for free, so it will be around for that use. You can read more about this decision on their blog here. Your service will be missed.
In the meantime I suggest teachers to download Firefox and install the Video DownloadHelper add-on. This will allow you to do what Zamzar was offering. It is pretty easy and allows some choices as far as quality and format conversion. It was just a lot easier with Zamzar. If you know of some quality services, programs, or add-ons/extensions be sure to leave them in the comments.
Technology in the Classroom 
Hey Patrick,
You may remember me from earlier in the year… I was starting out in an Edu. Tech class. Anyway, I have been using VideoDownloadHelper for several years and it’s a great utility. You also can extract audio from the files (mp3) as well — although that involves another small application to work in conjunction.
Another application that I use is MPEG Streamclip (www.squared5.com). It is a separate program but is similar in usefulness. The main selling point is conversion of MPEG files, but it can also download videos from YouTube and Google.