Damage caused by a wild animal such as a deer or bear are probably covered under your homeowners insurance, but damage caused by rats, mice or other vermin is generally excluded. Because a wild animal entering or attacking your home is not a problem that can be reasonably expected and prevented, the damage one may cause is covered under the same sort of risk protection as damage caused by a falling tree limb. If your stove was damaged by a raccoon that came in through the pet door, for instance, the costs of repair or replacement are most likely covered.
Rats and other rodents are considered vermin, not wild animals, and most rodent infestations are considered to be preventable. Because keeping the home free of such hazards is considered part of routine home maintenance, any damage caused by rodents could be considered negligence and specifically excluded from your policy. Not only does this mean that rat damage is not covered, it also means that damage caused by rabbits and other burrowing rodents is going to cost you out of pocket as well.
It is important to keep your home rodent free by putting up barriers where rodents might enter, such as blocking off eaves and installing fascia boards to prevent birds, squirrels, bats, mice and other pests from entering the home. Regular home maintenance includes testing for rodent infestations and setting traps or calling an exterminator when unwanted critters are found. Your insurance would cover a bevy of quail breaking a picture window, but it won't pay for a family of mice making your stove their home.