The Federal Aviation Administration has an extensive air traffic control system whose sole purpose is to keep aircraft separated. In high-density terminal areas, all flights are tracked by radar and are under positive control. Any aircraft flying in this airspace has a device called a transponder that allows controllers to identify the aircraft positively and its speed, direction, and altitude. Prior to flying in one of these areas by yourself, you will receive training on the proper procedures. Obviously, it's important that aircraft be reliable mechanically.
Aircraft are perhaps some of the best examples of over-design in engineering.
A factory-built airplane must meet rigid FAA design criteria and performance specifications. Each design is tested throughout its flight envelope, and a safety margin is then built in. For example, the structure of a typical training aircraft is certified to withstand 4.4 positive Gs. This means that if the airplane and contents weigh 2,000 pounds in normal level flight, the structure can safely handle up to 8,800 pounds in turns and pull-outs from dives, where the weight increases from centrifugal force. In routine flight, a pilot will usually not exceed 2 Gs.