1. The Futures Channel provides short, engaging videos with accompanying lesson plans on a wide range of topics. The site's main goal is to provide real world connections. I've used one of their videos to help teach ratio and proportion in class with great results. All you need is an Internet-connected computer, an LCD projector and speakers to bring many of your lessons to life. You can't legally download the videos, so you will indeed need to be online. There is a subscription service that makes high-quality, full screen versions of the videos available as well as even more resources, but I think what's available for free should be more than enough for most teachers' needs.
2. The second resource is Teachers' Domain, which culls clips from PBS programs like NOVA and Frontline for classroom use. As with The Futures Channel, clips are accompanied by lesson plans and activities. Many of the videos are available for download (depending on copyright issues) so you might not need to be online to use the videos in class.
Please share any other free video resources you've found useful in the comments. Preferably, the sites would be accessible from school for most, but if not, you have options: see my post How to Download YouTube and Other Internet Video for School Easily for starters. Thanks!