If you hold a private auto insurance policy, you probably are covered in the U.S., but not abroad, for loss or damage to the car, and liability in case a passenger is injured. The credit card you used to rent the card also may provide some coverage.
Car rental insurance probably does not cover liability if you caused the accident. Check your own auto insurance policy, the rental company policy, and your credit card coverage for the extent of coverage: Is your destination covered? Are other drivers covered? How much liability is covered if a passenger is injured? (If you rely on your credit card for coverage, you may want to bring a second credit card with you, as damages may be charged to your card and you may find yourself stranded with no money.)
Car rental insurance costs about $20 a day and up.
