Well, nothing is absolutely safe, but statistically riding a bike is more dangerous than flying, about as dangerous as driving, and actually a little safer than walking. The danger decreases with experience and sensible behavior. About half of all bicyclist fatalities are the fault of the bicyclist: they ran a ran light, didn't use lights at night, rode off the sidewalk into the street without looking, etc. If you ride predictably, signal your intentions, slow down in high-traffic areas with lots of intersections, and so on, you might die anyway, but the odds are very much in your favor; again, riding a bike is about as safe as driving.

One thing that I find really odd is that people keep bringing up this "bicycling is dangerous" nonsense. In most bike deaths, the bicyclist was killed by a car. Why isn't anybody seriously talking about how dangerous cars are? They're the things that are killing and maiming pretty much everyone that gets in their way out there, mostly people in other cars.