When renting a car you have about 3 options regarding insurance to consider:
1. You can purchase the insurance that the rental agency is offering. This option is usually touted at the rental agency as the best option if you want to keep an unfortunate accident involving their rental car off your record. I'm not certain that is true, but if so that would make it more appealing. The next reason why someone would consider this option is that it covers you for the (loss of use) lost revenue that the crashed car would have created for the rental company, if you hadn't wrecked it. Some kinds of auto policies and credit cards do not cover for this expense. The rental agency insurance is typically the most expensive way to cover your insurance need.
2. The next option for insuring your rental car is to deny all insurance offered by the rental agency and have your credit card cover the insurance risk. This option is typically the least expensive, because it is included by most credit cards for no additional cost, with exceptions and certain exclusions. Some of these exclusions and exceptions involve the make and model of the car and if it is rented in the USA or outside the country. Verify that the insurance provided by the credit card covers "loss of use".
3. The last of the common options for insuring your rental vehicle is to have your existing car insurance cover liability and damage. Your car insurance policy will not likely cover an overseas rental. However, if you have an umbrella policy it may very well cover the liability risk. You will need to check with your insurance carrier or agent for details on this. Regardless of where the rental will be driven, you will want to verify that your auto policy will cover for "loss of use" to the rental company, should it be needed.
My family just returned from a 3 week tour of Europe. Our family rented a car in Ireland and rented another when we drove extensively on and off the highway in the Netherlands, Germany and France. In both cases I planned ahead and learned that my Visa card, which I paid the rental expense with would provide insurance (including loss of use) on the vehicle models we planned to rent. My $1 million umbrella policy would cover any additional liability coverage, if it were needed.
It is important to think ahead on this matter, people are generally at greater risk of putting their insurance to work when they are driving an unfamiliar car in an unfamiliar area.