Videodropper is a free service for sending your favorite YouTube videos to your Dropbox account. When you link your Dropbox account to Videodropper you'll be able send videos your Dropbox for download. With the two services connected you simply copy the url of a video into Videodropper and it will be sent to your Dropbox account and from there you can download the video to your computer.
Applications for Education
If you work in a school that blocks YouTube access, Videodropper could be a great way for you to download and organize the videos that you want to show to your students. Of course, you would have to do that from home or some other place where YouTube isn't blocked. Then when you get to school you'll be able to open the videos from the download on your computer.
Whenever I mention downloading YouTube videos I like to remind folks that doing so might be a violation of YouTube's TOS. So use Videodropper at your own discretion.
Thanks to Doug Peterson for sharing Videodropper on Google+