The majority of car insurance policies do not cover you when you are renting a car, this sometimes includes courtesy cars so it is always best to double check with your provider. Most rental companies offer their own insurance for which you may be offered at a daily rate. If you are hiring the car long term, they may let you insure it yourself providing that you can provide them with adequate proof.
If you do take the insurance offered by the hirer, always be sure to read the small print. You will need to check who is insured to drive the vehicle and what the excess is should you need to make a claim. Often they will over you a slightly higher daily fee which will in turn waiver the excess on the policy. This is something you will need to weight up depending on what the excess is.