There must be a thousand variation on the 'phantom aircraft prank' but the one I saw was very nicely done from the comfort of the runway inspection vehicle.
The pranksters sat in the parked vehicle with the engine roaring (for that authentic aircraft sound) while they used the vehicle VHF and watched the confusion in the tower through binoculars.
They gave a couple of position reports and watched as the assistant went across to the teletype looking for the missing flight plan, they asked for clearance to land which they got, then asked for taxi clearance which they got while watching 3 or 4 people in the tower scan the runways looking for the aircraft. They asked if it was "OK to park here?" and watched as people came out of the tower and walked all around the outer balcony searching for the aircraft. They got an answer along the lines of "Park any of the marked positions".
The ATCOs said nothing about the incident to anyone but for months afterwards the callsign of the phantom aircraft could be heard wispered in bars and parties.