Just like any other food that contains essential oils, walnuts can go bad if left out for too long. This is why it is highly recommended that those who enjoy eating these nuts store them in a vacuum-sealed bag in the refrigerator or freezer so they will keep as long as possible.
By leaving walnuts sitting out on the kitchen counter for too long though, they can easily become rancid. This is because they have oils in them, so you will need to make sure that you go about storing them properly if you are not going to eat them right away.