Just like all other materials made from copper are prone to turn dull when exposed to air. Similarly, Pennies tend to corrode and set their colour to brown as copper atoms combine with oxygen molecules to form copper oxide called oxidation. The layer of green film can be seen once the oxidation happens over its surface. The green layer formed is known as patina.
Properties of Copper
Copper is used to making pennies to facilitate the process of minting pennies. Once you get to know the properties and tendencies of copper, it will be effortless for you to understand why pennies turn brown in colour.
Before 1980, only 5% of Zinc and 95% of copper was used to manufacture pennies. With time, the price of copper increased, making them use 95% of Zinc and 5% of copper. This change of formulae has resulted in the pennies corrode more quickly and easily, just because Zinc can be corroded swiftly compared to copper and change its colour to darker green or brown.
A noncorrosive oxidation
The pennies made up of copper alloy will not be corroded compared to the pennies made from iron. The only thing you will notice is that the pennies will slightly change their colour to brown because of the oxidation and copper’s inherent characteristic of attracting minerals. (See How Do Things Glow In The Dark?)
Why do you perceive brown colour over pennies’ surface but not green?
Since the patina is green, and the patina is formed over the copper surface after it gets oxidized and exposed to air, it still does not turn green in colour but brown. The sole reason is that copper tends to attract minerals from the dirt, making the copper alloy pennies turn brown in the long run. (See Why Do Pianos Have 88 Keys?)