I have had Progressive for years and have never had any trouble. My car got plowed into by a deer, and Progressive was reasonable to deal with. Their rates are also about the best I can find. We bundle in our home insurance (through some licensed third party) and save even more! Our rates just actually went down this past 6-month period which was a pleasant surprise.
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.
Collision and comprehensive insurance are two optional types of auto insurance where your insurer pays for repairs to your vehicle. While there are other optional auto insurance coverages, liability, comprehensive, and collision are three of the most common. These coverages work hand-in-hand to repair or replace most of the damages to your car. It's important to know the difference, and make sure you're adequately covered.