How dangerous is rock climbing?

Any outdoor sport involves some element of risk. If you learn rock climbings skills from a knowledgeable instructor, are careful to follow established safety procedures, and choose to do only top-roping (in which case there's always a rope going from you to a higher belay), the risk is small. Lead climbing creates somewhat more risk, but choosing well-protected routes that fall well within your abilities, the risk still falls within what many people consider an acceptable range.