There are several metals that oxidize or react with your skin to produce a discoloration. You can get a noticeable green ring around your finger from wearing a ring made using copper. Some rings are pure copper, while others have a plating of another metal over copper or the copper may be part of the alloy (e.g., Sterling silver). The common green color is not harmful of itself, though some people experience an itchy rash or other sensitivity reaction to the metal and may wish to avoid exposure to the metal.
A common culprit is silver, which is found in sterling silver jewelry, plating for inexpensive jewelry, and as an alloying metal in most gold jewelry. Acids cause the silver to oxidize, which produces tarnish. The tarnish can leave a dark ring on your finger.
If you are sensitive to metals, you may see a discoloration from wearing a ring containing nickel, though most likely this will be a red ring and may be associated with inflammation.
How to Avoid Getting a Green Finger from a RingEven silver and gold jewelry can produce a discoloration, so advice for avoiding a green finger isn't as simple as just avoiding cheap jewelry. However, certain metals are less likely to turn green than others. You should have good luck with stainless steel jewelry, platinum jewelry and rhodium plated jewelry, which includes nearly all white gold.
Also, you'll greatly reduce the chance of any ring turning your finger green if you take care to keep soap, lotions and other chemicals away from your ring. Remove your rings before bathing or swimming, especially in saltwater.
Some people apply a polymer coating to their rings to act as a barrier between their skin and the metal of the ring. Nail polish is one option. Be aware you'll need to reapply the coating from time to time, since it will wear away.