Comprehensive car insurance covers damages from an "act of God," or events that are not caused by a car driving into something else. An "act of God" can include things like damage from a heavy tree branch falling on your car. Since you have no control over when or why a tree branch would fall on your car, this kind of accident would be covered under your comprehensive policy.
Insurance terms, definitions and explanations are intended for informational purposes only and do not in any way replace or modify the definitions and information contained in individual insurance contracts, policies or declaration pages, which control coverage determinations. Such terms may vary by state, and exclusions may apply. Discounts may not be applied to all policy coverages.
If you have paid off your car, comprehensive coverage is optional. It may be a good idea to find out the Kelley Blue Book value of your vehicle. Would you be able to pay that amount to repair or replace your vehicle if it were stolen or damaged in an accident? If you can't afford to pay much out of pocket, then buying optional coverages, like comprehensive coverage and collision coverage, may be a smart investment.