Cheap jewelry gets a bad reputation for turning your skin green. This is simply a chemical reaction between certain metals and your skin. Most often, this comes from nickel, alloys (mixed metals) and copper lead jewelry. Some people even have this problem with sterling silver and 14K gold when it's mixed with other metals.
If your skin tends to turn green easily, try to find rhodium-plated jewelry, which prevents the reaction. Also, avoid any jewelry that causes a reaction during hot days and while swimming as this can cause oxidation and the green ring.
Many people also paint a thin coat of clear nail polish on the part of the jewelry that touches the skin. It doesn't always work, but it's worth trying.