When I served as Priest Secretary and Master of Ceremonies to the Bishop, I also served as the Associate Director of the Office for Vocations. The latter position largely entailed my speaking with the Bishop to the Confirmation candidates about the discernment of one's vocation.
We would typically meet with the confirmandi for about thirty minutes before the Holy Mass. Bishop Paprocki would begin describing the symbolism of the priestly vestments and the insignia of a Bishop, after which I would talk about discernment. The Bishop then opened the floor, if you will, for a Q & A session between him and the confirmandi.
One of the most frequent questions - aside from "Who is your favorite hockey team?" - was, "Why do you wear your ring on your right hand?" It seemed odd to the candidates because they are used to seeing wedding rings worn on the left hand.
The Bishop would then explain that it is customary for Bishops - and Doctors, if they so choose - to wear a ring on their right hand. He also mentioned that in Poland, spouses wear their rings on the their right hands and not on their left (when they are widowed, they move the ring to their left hand). Neither of us really knew the reason why spouses in the U.S. wear rings on their left hands (or why spouses in Poland wore them on their right, for that matter).
The usual answer given to such a question is that the left hand is closest to the heart. It's an answer that comes too easily and never quite seemed right to me. As it turns out though, it isn't too far off.
I've been reading Michael P. Foley's article, "Coins and Care-Cloths: The Mystagogical Value of Traditional Wedding Customs" in Antiphon [18:2] in which he writes of the wearing of wedding rings:
In those locales where rings and coins were differentiated, each object assumed its own symbolic importance. The ring, as we have seen, was interpreted as a symbol of mutual fidelity and loving union. It was either placed on the right hand to affirm the dignity of marriage (the right hand being higher in standing than the sinister left); or it was placed on the ring finger of the left hand because it was believed that a vein ran from this finger straight to the heart. In areas where the priest gave the ring to the groom before the groom gave it to the bride, the rings could also signify that the Church approves of and seals the love of this couple (120-121).
Here we have, then, the explanation of both customs for the wearing of wedding rings.
Foley mentions as a source for this custom the writings of Saint Isidore of Seville (560-636). Since he did not directly quote the holy bishop, I looked up the cited passage. It reads as follows:
The symbolism presented here is excellent, but it turns out, according to my friends in the medical field, this vein - the vena amoris - does not actually exist.This is the reason that first of all a ring is given by the husband to his wife; this is done certainly either as a sign of mutual faithfulness, or even better, that their hearts be joined by this pledge. Consequently, the ring is placed on the fourth finger so that by the vein in it something of the blood, as it is carried, will arrive all the way to the heart. In former times, however, nothing more was given by one, lest the plurality [of signs] divide the one love (De Ecclesiasticis Officiis, 2.20.8).
When he refers to the wearing of a ring by a bishop, Saint Isidore does not mention on which hand he wears it, but explains why a bishop wears a ring:
He is also given a ring as a sign of episcopal honor and for the sealing of secrets. For there are many things that, keeping hidden from the worldly and the less intelligent, priests establish as "under the seal" lest the sacraments of God be exposed to those who are unworthy (2.5.12).