There are a number of countries in the world who actually wear their wedding rings on their right hands. For example Greek Orthodox members who get married wear their rings on their right hands after they get married, and prior to getting married they will wear it on the left.
There are many other countries who wear their wedding rings on their right fingers: Norway, Portugal, Spain, some of the countries which made up the former Yugoslavia such as Serbia and Croatia, Russia, the Ukraine, Norway, Bulgaria, Poland Austria, Denmark , Germany, and of course Greece. All of these have very widespread practices, except for Roman Catholics, who do the opposite. In Belgium (at least within the Dutch speaking part) you will wear a it on the left hand, but in the rest of the country, it is typically the right.
In a traditional Jewish ceremony, the groom will place the ring on the bride's index finger, and not the ring finger of either hand at all. Today the ring is often transferred from the index finger to the ring finger after the ceremony (especially in the West), and most Jewish grooms also wear a wedding ring. The reason that Jews use the index finger, is that they believed that it was the most important finger.
Indian brides are also quite confused as to which finger they are to wear the ring on. According to Indian culture, the left hand is less important than the right. But many will wear the ring on the left anyway.