Is it necessary to buy Rental Car Insurance even though i have my car insurance policy with me?

I have a car and have taken Auto insurance for it. Now my question is if i take a rental car, then my auto insurance policy for my car covers it or i need to take separate insurance for the rental car? When i took the auto insurance policy, they have taken my car details and its present in the insurance card also.... show more I have a car and have taken Auto insurance for it.
Now my question is if i take a rental car, then my auto insurance policy for my car covers it or i need to take separate insurance for the rental car? When i took the auto insurance policy, they have taken my car details and its present in the insurance card also.
If i need to take insurance for rental car, what type of insurance do i need to take excluding my auto insurance policy coverage that applies to all cars?
Also if i am driving someone else car, will my insurance cover if there is any accident i have made?