Lots of animals can eat crops. I've had significant damage caused by a badger, for instance (managed to hunt it down eventually, but it took many attempts).
Traps can provide protection to some extent. However, traps suitable for small animals will do nothing to stop medium sized animals, and traps for medium sized animals will do nothing against small animals (fences will keep large animals out, although bears can smash them if they find a reason to do so). Small and medium sized animals have no problems passing through fences.
Also note that while trees block passage for ground based animals, they're passable by birds.