If you already have full coverage - meaning comprehensive and collision - with your normal auto insurance you should speak to your insurance agent to see if this will extend to your rental car. Some insurance companies may not allow this or limit the amount of coverage you would have on the rental car.

If you do not have comprehensive and collision coverage on your personal car you might want to add it so that it will cover the rental car period, again speak to your insurance agent to make sure this would work. Another option is to obtain a 'non-owners' policy which might be more cost effective than the insurance options given to you at the rental car counter. Many insurance companies only set up non-owner policies for liability so you might have to search to find one that would allow full coverage.