The US is one of the least dangerous places in the world, in almost every possible way.
Most of those things are so rare that they don't have much of an impact. The only thing common enough would be accidents, which are the #5 cause of death in the US. How many accidents we have compared to other countries though, I'm not sure. That is a good question.
For reference, here's what is killing us (
2009 stats from the CDC):
Heart disease: 599,413
Cancer: 567,628
Chronic lower respiratory diseases: 137,353
Stroke (cerebrovascular diseases): 128,842
Accidents (unintentional injuries): 118,021
Alzheimer's disease: 79,003
Diabetes: 68,705
Influenza and Pneumonia: 53,692
Nephritis, nephrotic syndrome, and nephrosis: 48,935
Intentional self-harm (suicide): 36,909