Unpiloted aircraft that fly off on their own is actually not a myth, mistakes do happen on the tarmac and sometimes pilots forget to turn off the throttle. In most cases, the unguided planes shoot across an airport until they crash into a line of light planes, a hangar or some parked cars. But on several occasions, they have followed the laws of aerodynamics and lifted off, as a result flying for several hours on their own.
In 2001, an Aeronca Champion plane took off from an airstrip in Sonoma County, California without a pilot following an error and it just flew off until its fuel tanks ran dry. It took days to find the crash site, luckily it did not hit another plan while flying. And in 2009, a vintage Stampe biplane took off from an airshow at Goodwood, England! This one crashed five minutes later into some trees.
Of course, unpiloted planes landing is a completely different story, this is a much rarer event. They were a couple of stories of B-17s landing themselves in fields in England after their whole crew had parachuted out, but those stories have never really been proven. And it seems a bit odd that a huge plane like a B-17 would set its landing gears in motion by itself.
The most notorious ghost rider of them all is known as the cornfield bomber, an unpiloted supersonic jet fighter that flew unpiloted and also landed successfully. It is a story that comes out of U.S. Air Force lore, a Convair F-106A Delta Dart that landed without any problems in a Montana farm field on February 2, 1970.
The pilot had to parachute out of the plane after it went into a flat spin, yet after the pilot parachuted out, the plane recovered itself and kept flying. This happened during a training exercise where the pilots went into quite complicated maneuvers to evade each other, and Lieutenant Foust went into a flat spin which is normally known to be unrecoverable.
But after choosing to eject, the plane decided it was done with flat spinning and continued to fly, which spawned the fabled radio line “Err, Foust, you better get back in it.” Of course, that proved impossible. Luckily, the plane landed without causing any harm in a farm and the pilot parachuted safely to the ground.