If you happen to work in a school that does allow you to access YouTube, TubeChop may be of interest to you. TubeChop gives you the ability to clip a section from any YouTube video and share it. This could be useful if there is a section of long YouTube video that you want to share with your students. One such instance could be if you want to show students studying public speaking a section of commencement address as a model.

Here are some related resources that may be of interest to you:
Splicd – Create Your Own Video Segment
170+ Intelligent, Educational YouTube Videos
YouTube Edu – 100+ Colleges on YouTube