Yes, but its shelf life is so long it can reach up to months at room temperature without spoiling or become contaminated by bacteria or fungi because of its low moisture and high oil content even if its container is opened.
Peanut butter won't go bad like perishable food will. It will, however, go "rancid," meaning it will have an off flavor. If this happens, it should be discarded. Keeping it refrigerated is highly recommended.