This is a natural condition and not at all dangerous. Yolks naturally contain some small amounts of sulpfur (which is released when they are cooked - or when eggs rot, hence the particular smell of "rotting eggs". This sulfur combines with hydrogen present in the egg whites and that produces the green ring. It can also be causes by a high amount or iron in the water (again, not dangerous).
A green-blue color is usually caused by simply cooking the eggs too long.
Many state university extension services recommend the following cooking method for hard boiled eggs to avoid the green rings: The following comes from the University of Wisconsin: