An Aerogal Boeing 767 attempts to land on the wrong runway at New York’s JFK airport, nearly colliding with a Jetblue rolling for take off. The tower air traffic controller sorts it out and a collision is averted. Audio from Liveatc.net.

The Aerogal had been cleared for a Parkway Visual Approach (Canarsie Approach) to runway 13L and had subsequently been cleared to land on 13L. The procedure resembles circling procedures such as the legendary Kai Tak IGS to 13, albeit with less drama due to the absence of mountainous terrain.
Once at the Canarsie VOR, planes fly a 041 heading along the Shore Parkway (the main visual reference) and then begin a right turn to either 13R or 13L (typically 13L is used because it is a wider, easier turn). The primary visual aid, especially at night, is provided by clusters of lead-in lights. The first cluster is approximately 2 miles from the threshold of 13R.
When cleared for 13L, pilots begin a slight right turn at the first cluster, then follow two more clusters and initiate a tight right turn to line up with the runway, where the fourth and last cluster of lights is located. This video gives you an idea of what it looks like at night: /> Now, to line up for 13R, pilots must have initiated a tight right turn at the first cluster to enter a 2 mile final. For the Delta pilots on the ground to spot the mistake, the plane must have been already lined up with 13R, so it could not have been much more than a mile away. By the time Delta warned the tower and the controller issued the go-around, the Aerogal must have been quite close to the threshold.