When you rent a car, you are liable for injuries and property damage you cause to others, and damage to the rental car whether it’s your fault or not. With some restrictions, your insurance policy will cover you in your policy territory (United States, its possessions and territories, and Canada) if you injure someone or their property. In most cases, your auto policy will also cover damage to the rental car, but you must carry comprehensive and collision coverage on at least one of your covered autos.
If you plan on your credit card covering damage to your rental car, read the fine print. Some only provide coverage after you prove there is no coverage under your personal policy. Some cards actually have dollar limitations and very restrictive coverage.