Insurance agents are asked this question regularly. The answer, unfortunately, is not black and white. It depends. Here are a few things for you to think about when renting a car.  

1. Vehicle coverage - Do you have comprehensive and collision coverage on a vehicle you own? If so, this coverage will extend to your rental car. If not, then there is no coverage to extend to cover the rental vehicle. Keep in mind, in the event of an accident, you would still need to pay your comprehensive or collision deductible to your insurer before the insurer would cover the damage to the rental car (just like in the event of a comprehensive or collision loss to your own vehicle).  
2. Diminution in value - If you wreck your rental car, the rental car company can claim that the market value of the rental is now diminished since it has been in a wreck. You could be responsible for this diminished value and be required to pay the difference.  
3. Loss-of-use - If you wreck your rental car and the rental car is in the shop for repairs, the rental car company could claim they lost business. This means they can require you to pay for “renting” the car while it is being repaired. *Some carriers have coverage options that will cover this. However, there are often limits on how much the insurer will pay per day as well as a maximum they will pay out. This coverage also may only extend to the named insured and spouse and not other resident relatives, such as licensed insured children, even if they are on the policy.  
4. Ease - If you do not purchase rental car insurance and do get in an accident, the claims process is often more time consuming than if you buy the rental car insurance. The rental company can also put a hold on your credit card until the accident is settled. Even more shocking, is that some states allow the rental company to keep the renter in the state until the claim is settled, even if the renter was not the at fault party.  
5. Vehicle value discrepancy - In the event of an accident, the rental agreement may require you, the renter, to reimburse the rental car company for the full value of the vehicle. Most insurers cover the lesser of the actual cash value of the vehicle or the cost to repair or replace the damaged vehicle.   
6. Extra expenses - The rental agreement may make you, as the renter, pay for any extra expenses. This could include towing, storage, or impound fees. The good news is, if you carry towing on your personal policy, this typically extends to your rental vehicle.  
7. Claim vs No Claim Reported - If you have an accident in a rental vehicle and if you have purchased the rental car insurance, the accident will likely not affect your future insurance premium as this accident is not reported as a claim on your personal insurance policy.  

Ultimately, rental car insurance has a high daily cost, however, the cost can potentially be much higher for an individual that chooses to rent a vehicle without the rental car insurance. It really comes down to your risk tolerance.  

*Please note that it is always important to talk to your agent regarding your specific policy as contract language can differ between carriers.