The answer is generally no, unless you don't have car insurance of your own. Chances are that the individual car insurance you have on your own car also covers rental cars. Check your own car insurance policy language to see if there is a provision that talks about this.
Other Sources of Coverage
You may also want to check your homeowner's insurance policy to see if you have rental car insurance coverage under that policy, as many do. If you're traveling for business, check with your employer about their insurance. Many employers whose employees are required to travel buy insurance for this very purpose.
You should also check with any of your major credit cards. Often times, credit card companies will provide rental car insurance coverage, if you use that card to rent the car. This language is often spelled out in the tiny print the credit card company sends you with your card.
Bring Your Documents Along
Oftentimes, people leave these types of documents behind when they travel. However, it might be a good idea to do so if you know you're going to be renting a car. Rental car companies may try to pressure you into purchasing their own rental car insurance coverage by telling you that it's the law or that your own insurance won't cover the rental.
This typically isn't true. If you have your policy with you, be it the credit card contract or insurance policy, you can show this to the car rental representative as leverage to avoid buying their car rental insurance coverage. This should end any arguments or disputes over coverage, which is especially helpful after a long day of traveling.