What is the name of the type of insurance that protects a person in the event of a certain type of accident such as an automobile accident or a plane crash?

I believe that you are referring to an accident policy. There are also some that state they will only payout if you die while traveling on public transportation. In my opinion, accident policies are not worth the cost even though it is usually small. You are better off taking the money and purchasing as much life insurance as possible instead of the accident only policy. Life insurance will pay no matter how you die and it is money you can count on your family getting. You don't have to die in the right way to protect your family. What if a commuter train you are own crashes but you survive the crash only to die a few minutes later from heart failure. The accident policy will not pay but the life insurance would pay and without any problem.