Very safe and very fun. I never leave home without mine, because it is pretty cheap insurance. But cycling must be put into relationship with other risks. Statistically, stairs are a far more dangerous place than bicycles. Bathtubs are a far more dangerous place.
Cycling is safe and fun, cycling is safe and fun.
That's the point that the League of American Bicyclists makes in Effective Cycling. These are skills that prevent crashes, not just mitigate the danger. And perhaps more importantly, there is no false sense of security imparted in developing Effective Cycling skills, only the confidence gained from understanding your environment. Live long and prosper.