If you did not purchase the 'loss damage waiver' coverage from the rental agency and do not have your own auto insurance that would extend to the rental car then you could be personally liable for any damage you caused to the rental car as well as any damage or injuries you may have caused to others.
The rental car contract should state what you are responsible for if the car is damaged or totaled out in an accident. If you fail to carry insurance either from your personal auto insurance carrier on the vehicle or purchasing coverage from the rental car agency then you are going to be held personally responsible if in an accident.
Even if you do have insurance coverage for the vehicle itself you may still end up owing for the time the vehicle is out of service for the rental car agency since that is not normally covered by a loss damage waiver or your own Collision coverage.
Before renting a car make sure that you have proper Liability and Physical Damage coverages on it so that you are protected from being held liable for damages if you are in an accident.