Liquid Image offers combination products like this diving mask with a camera incorporated.
AEE has a full line of small, mountable cameras, including this 3D model with HD video.
The Midland XTC-300 films in 1080p, and is displayed here on a handlebar bike mount.
This camera by Contour is shown with a Ram mount on the hood of a car.
Have you ever tried diving with an underwater camera? It's easier to swim using both hands--which is why having your camera attached to the mask makes great sense here.
Another sports camera.
Here are a few other AEE cameras.
If you snowboard or ski and want to review your downhill techniques, this in-mask camera model from Liquid Image will do the trick.
With AEE's add-on wireless footage review system you can quickly see what footage you've captured and reshoot if need be.