The one study I've seen that looks at the net health effect of cycling came to the conclusion that cycling is a net benefit. Loads of bicycling advocates promote this to suggest that cycling is in general a net benefit for you health. Unfortunately for North Americans, the data in the study came from Europe. Cycling is much safer in Europe. I am not aware of any analysis using data from North America, and I'm unsure whether such an analysis would come to the same conclusion.

With this being said, I ride a bike for transportation. I read studies on safety and actively try to minimize my risk. This includes minimizing my mileage, as the risk is per unit distance. So far, so good. I haven't been in a real crash yet in 4 years of commuter cycling, though I've had plenty of close calls. Worst I can say is that I did once hit a pothole and fall over, but there were no lasting effects.