At an airport I worked at once we had a report of someone wandering around one of the taxiways.
Turns it out it was a young lad with learning difficulties on his way to his first job who had been running late and decided to take a short cut across the airport, runway and all.
I can't remember how he got through the perimeter fence but it was pretty impressive.
Also had those nutty Plane Stupid protestors handcuff themselves to a taxiway and start playing crazy golf once. Their argument would have carried a shred more weight had it not later transpired that a few of them had got to the protest the day before by flying up for it...............
Edited because I just remembered another one....At another airport I worked at, we had a call reporting people seen running from an aircraft. Turns out that a flight that had arrived from Paris had landed and begun de-planing when 3 oriental gentleman decided to make a run for it on the walk from the bottom of the aircraft steps, to the terminal building. They managed to jump into the river and never heard if they were found.