For http://optional.is/contest/ the winners are selected based on being closest to a random point on the globe. The equation used to compute the distance is the Haversine formula.

http://en.wikipedia.org/wiki/Haversine_formula

In full disclosure, the code used to compute the distance has been open sourced.

To use this in your own projects, you simply include the file
include('haversine.php');

And pass it a pair of lat/lons
$distance = haversine($lat1,$lon1,$lat2,$lon2);

The distance in kilometers is returned.