This is a project which will literally pull your mind out from your head.
The whole idea is to view ourselves live in 3rd person. A camera will be mounted to ourselves looking at us from behind. A video goggle setup will then allow us to only see ourselves in 3rd person.
We will explore how to make a setup like this for relatively cheap. We'll look at other permutations, such as transmitting the data, using the setup in paintball with a marker mounted camera, and so on.
[edit: check out step 10 for the 3rd person view]
Step 1: The Camera's
As the setup goes, really any camera with a video output will do. I have a small video CCD camera with the component video and audio output. That ran me about $60. You can get cheaper ones if you'd like. If you really want to play with this, I would suggest getting a good camera. After having done it, I would prefer a higher quality camera.
Some digital cameras or camcorders can do video out as well. That will work, as long as it is live.