Actually, in medieval times the ring was usually worn on the right hand - this was due, I understand, to a passage in the Bible.
Protestants started to switch hands in order to break away from the Catholic tradition. Catholic Bishops and the like still wear their rings on their right hands in the old fashion, and I seem to remember that central European Christians (or is it Orthodox Christians?) still wear their wedding rings on the right hand.
Edit: Mind you, the whole subject is obscure. The Romans, for example, believed in the Vena Amoris, a vein in the fourth finger of the left hand which ran straight to the heart, which is another cited source for the western sinister "ring finger".