If you are speaking of physical damage coverages such as collision and comprehensive then they do cover such incidents as you described. Comprehensive covers your vehicle for such things as when your vehicle is stolen, damaged by flood, fire, vandalism or hits an animal. This coverage will allow you to have your car repair or if deemed a total loss compensated for, after you pay your deductible.

Collision covers when your car hits, or is hit, by another vehicle or object. Thus if the accident was your fault and your car is damaged or totaled you insurance policy should cover the vehicle, again after the deductible is paid. If you are ready to shop for these types of coverages you can get cheap car insurance quote.