There are probably others, but often we see only the damage. As I mentioned, woodpeckers are protected. When damage is severe it is possible to obtain a permit to eradicate them. That is a last resort effort. If it comes to that a small caliber rifle or BB gun works if your a good marksman.
Snap traps placed under the hole they are working on is also effective if death is the only way.
Effigies are effective depending on if the pecking is localized. These consist of owls, snakes, huge eyes, etc. They are not very becoming especially if the woodpeckers are working on the front of the house. We've found that ribbons attached to a slender pole and attached near the damage will repel the woodpeckers. Any amount of wind will create movement thus scaring the birds.