A flight instructor once told me that flying single-engined piston planes was statistically about as dangerous as riding motorcycles, which I assume is more dangerous than driving cars.

Greenspun has some data: http://philip.greenspun.com/flying/safety

Watch out for airplane stats that count accidents/mile. Accidents/hour is a much more relevant measure.

Is it, though? But if I consider the safest way to get from A to B, miles seem more relevant?

To determine the safest way to go from A to B, you need to incorporate both distance and time accident rates, no?

I'm sure walking is actually a pretty unsafe method, when you consider distance.

I wonder how business jets and very light jets compare to big airliners of similar ranges.