Peaches can in fact be frozen and it is recommended that you remove the pits before doing so. You will also want to put them on a piece of wax paper until they are completely frozen. After the peaches have become completely frozen, you can feel free to take them off the sheeting and put them into storage baggies.
By freezing your peaches, you will be able to keep them from going bad and growing mold. While putting your peaches in the vegetable crisper inside your refrigerator will keep them from going bad, it will only work for so long until they are no longer edible.