The History channel had a brief segment on what happens when you are beheaded during one of their shows about the progression of the tools of execution.

They described the situation as the (now disembodied) head senses the feeling of falling and makes an effort to stay itself. But not being connected any more to the body, it continues to sense the falling motion, and for a brief period adopts an expression similar to someone in free-fall.

They also indicated that the brain bleeds out rapidly, and consciousness is lost within about 10 seconds.

I guess that ain't a bad way to go....

As for hunting, I make it a point to make the most rapid knockdown possible for several reasons:
- Most importantly, an instant kill relieves any suffering on the animal's part
- No panic means no stress hormones, which means better meat
- clean kills keep all of the animal's carcass useable