Paintball is very safe as long as you follow the rules and use common sense. Any severe injuries come from people simply not following rules - usually removing their mask when they shouldn't. There are, of course, minor injuries such as strains and sprains that are associated with all action sports and paintballs can leave minor bruises.
As a whole, paintball is very safe, does not lead to major injuries and only hurts a little bit. In fact, based on severe sport-related injuries that lead to emergency room visits, paintball is safer than bowling.