How high a plane flies depends on the plane's construction and intended use. Most commercial airliners fly at a cruising altitude between 25,000 and 40,000 feet above mean sea level. The Concorde jetliner has a typical cruising altitude of around 45,000 feet. Military planes can typically fly at much higher altitudes; the Stealth Bomber has a 50,000 feet cruising altitude.
Planes are typically certified to be safe to fly at a higher altitude than the cruising altitude. Keeping the cruising altitude lower than the maximum flying altitude gives the plane's captain the option to move the plane safely to a higher flying altitude if necessary. Higher flying altitudes help the planes to travel more efficiently with less wind resistance. Higher altitudes also decrease the chances of hitting air turbulence. Once a commercial airliner reaches around 40,000 feet, the engines are at a power level just above idle, allowing the plane to fly while using a minimal amount of fuel. If a plane travels at a high speed at too high of an altitude, unless the plane's engines are equipped with oxygen, there is not enough oxygen in the air to burn jet fuel at a rate to keep the plane at that height.