The rental-car clerk will offer you a collision-damage waiver (sometimes called a loss-damage waiver), which can cost $10 to $20 per day. The CDW shields you if the rental car is damaged or stolen. But as long as the rental is for personal use and you have collision coverage in your own auto-insurance policy, you’re covered without the CDW (with the same deductibles that apply to your own car).
Your credit-card benefits supplement your auto coverage. Most cards will pick up your deductible, and premium cards offer beefier coverage. (Keep in mind that credit-card protection doesn't include liability. And if you've dropped comprehensive or collision coverage on your auto policy, the rental car will be covered by your credit card if it is stolen or damaged in an accident.