Yes, butter does spoil.
As a dairy product, butter has a relatively short shelf life. Butter is made with about 80% fat and 15% water. Exposure to bright light and air break down the fat molecules that make the butter rancid so butter that is left out at room temperature will begin to degrade in odor and taste within a few days compared to weeks when stored in a cool dark place.
How to Store Butter
If packaged and cared for properly butter will last for one to two weeks in a refrigerator at a temperature set below forty degrees Fahrenheit. Butter absorbs odor so ensure that it is wrapped properly. For best results keep unopened butter in its original packaging. Butter that has been opened should be returned to the refrigerator in a waterproof, airtight container. Do not wrap butter for storage in aluminum foil as metal hastens food oxidation.
Butter absorbs odors readily so should be stored in an airtight, moisture-proof container like a freezer bag. Butter will keep at 0 degrees Fahrenheit or below for six to nine months. When you are ready to use the butter, thaw it in the refrigerator.
How to Tell If Butter Is Rancid
Rancid butter is evident in the bitter taste and foul odor. A stick of butter that has gone bad will also have a translucent look and be darker in color than when it purchased fresh. If butter has been minimally exposed to heat, light, and air it may be salvageable. Dark yellow patches will be evident where the butter has had the most exposure. These can generally be removed to salvage the rest of the butter that can still be enjoyed.