In the United States, comprehensive and liability coverages will typically carry over and can extend into rental cars, so you may already be covered. Your credit card company may also provide you with some secondary coverage, so it is a good idea to check with them too.
If the car you are renting is of similar or lesser value to your vehicle, your insurance coverage will most likely be adequate for your rental vehicle. However, if you are renting a car that is of higher value than your personal car, you may want to purchase the additional auto insurance that is offered by the rental company.