Let me throw in my 2 cents as the owner of an independent insurance agency. The typical auto policy will cover damage to the rental car with the same deductibles as you have on your most liberally covered car. The rental generally must be for less than 30 days and in the US or Canada. There are two critical areas where the typical policy will not cover you:
Loss of use. If you get in an accident and the car is laid-up for a period of time, the rental company will continue to charge you for the daily rental.
Dimunition of Value. Yes, that's really a word. The rental company will claim that because there is now a Carfax report showing an accident, the re-sale value of the car has dropped...and you have to pay for that loss of value. This can run into the thousands!
Disclaimer - check with your insurance company or agent for details regarding your policy.