Rust, tarnish, and verdigris (and the oxide coating on old pennies) all result from the chemical reaction of a bare metal surface with something in the air. That something may be oxygen, water, carbon dioxide, another chemical, or some combination. Rust forms when iron is exposed to air and moisture (water). If a piece of iron is left outside, it will eventually rust away to nothing. If you don't want an iron object to rust, you need to protect its surface by painting it or coating it with another metal, such as zinc (called galvanizing). You might think that silver tarnish also forms from a reaction with oxygen, but tarnish actually needs both oxygen and sulfur to form. Tarnished silver may look ugly, but the tarnish actually protects the silver underneath from further reaction!
Verdigris (VUR-di-gree) is the green coating that forms on copper or other copper-containing metals, such as bronze or brass. It forms from the reaction of copper with oxygen, carbon dioxide, and chloride (near seawater). Perhaps the most recognizable American example of verdigris is the Statue of Liberty. She is made of copper, and was originally brown! But over time, a verdigris coating has formed, giving her the familiar green color. You can sometimes see other examples of verdigris on copper roofs on old buildings, or on outdoor statues. Keep your eyes open, and you may spot some verdigris in your own neighborhood!