Your brain is your moneymaker--put out your hands!
I used to reach out my hands when falling, but now I tuck them in and lead with my shoulder. that was my first major fall, but it's something that I would repeat to myself in my head while riding. In the aforementioned case, I was falling sideways and forwards. I suppose if I were leading with my head I would try to break the fall with my hands. I don't know; it all comes down to muscle memory, subliminal reaction, and how bad I'm freaking out at the time.
Martial arts training (judo would be a good one) can help a lot here.
There are also a lot of context specific tricks you can pick up. Like if you fall skiing or snowboarding make a fist when you put your hand down instead of falling with an open hand. A fist vs. open hand won't make much of a different on snow, and the fist will stop fingers/thumbs from catching and breaking. In addition the wrist is less likely to break.
On a side note, I've actually been thinking of taking up martial arts training.