http://www.amazon.com/Spy-Gear-Panosphere-360-Degree-Cam/dp/...
I have two of them and while the native recording is very fish-eye, the software that comes with the unit functions fine in focusing on a specific point.
With a 32 GB card and full charge, I think I've gotten about 45 minutes of recording. Might not be good for daily use, but for recreational outings it might be usable with some customization (e.g. super glue a mount to it). I've got one mounted on a swivel clip from a clip-on guitar tuner that broke and it's been a neat tool.
Edit: Example footage of using the camera: https://www.youtube.com/watch?v=cBpEGw3tTZ8
Unfortunately after about 2 years the plug on my XD1080 stopped working so I can't reliably charge it :/ I'll probably replace it with the Prime X when my budget allows.
Lower profile than strapping a GoPro to your head and cheaper too.