Most of my falls were related to inattention. I've had a number of significant failures, but only one dropped me to the road. That was the time my crank arm broke while climbing. The time when my left side bar broke at the stem was not dramatic probably because I was climbing and pulling up on the bar. I've had brake cables break (or as some here say "break cables braking") but again not much drama. Discounting the variety of minor equipment failures, like flats, dropped chains, shifter cable breaks, broken spokes, etc. catastrophic failures are not all that common.