The edge of space is 62 miles, or 327,360 feet. Air density is required for planes to fly and maneuver, and they need special designs to operate at altitudes higher than 54,000 feet. The oxygen level is 1 percent of what it is at sea level at that altitude and air density is low. As a result, flaps and elevators don't respond as well as at lower elevations.
The Virgin Galactic is a project that aspires to take passengers on a short trip into space. It can fly to about 68 miles high, which is enough to feel weightlessness.
The SR-71 is a military plane that has a cruising altitude of 85,000 feet, or 15 miles. It can fly as high as 125,000 feet, or 23 miles. Some of the information regarding this plane is classified.