You could wait for air resistance on the elevator to take effect as it accelerates, but I imagine that its terminal velocity would be quite high so this might take a while.
Interestingly, Otis is famous for his invention of the elevator safety brake. http://www.ideafinder.com/history/inventions/elevator.htm
There are almost no cases of an elevator's cable just snapping and going into downwards free fall - with the exception of (possibly) during 9/11 and an incident in 1945 where a bomber pilot rammed a building. The elevator operator dropped 75 floors but miraculously survived:
> One of them fell from the seventy-fifth floor with a woman aboard—an elevator operator. (The operator of the other one had stepped out for a cigarette.) By the time the car crashed into the buffer in the pit (a hydraulic truncheon designed to be a cushion of last resort), a thousand feet of cable had piled up beneath it, serving as a kind of spring. A pillow of air pressure, as the speeding car compressed the air in the shaft, may have helped ease the impact as well. Still, the landing was not soft. The car’s walls buckled, and steel debris tore up through the floor. It was the woman’s good fortune to be cowering in a corner when the car hit. She was severely injured but alive
I think a good solution would be to cross your arms and place them under your head. I'd gladly suffer two broken arms to cushion the impact on my cranium.
