According to tradition, the wedding ring is worn on the left ring finger because the vein in the left ring finger, referred to as the vena amoris was believed to be directly connected to the heart, a symbol of love.
A guy I know who is Greek wears a ring on the 3rd finger left hand but he is not married. He is engaged. I am told that this is done when Greek people get engaged (men and women) the rings are blessed by a priest and worn on the left hand until the wedding when the rings are changed to the right hand.