Will your health insurance cover medical expenses if you are injured in a car accident?
As with anything regarding health insurance, it depends.
Generally speaking, in an auto accident the question about medical benefits is secondary to providing the best care for the accident victim. After the emergency has passed is the time for figuring out who pays for the medical expenses.
Often health insurance is asked to pay first. However, health insurance companies have a program called "subrogation" that seeks to ensure that the responsible party pays for their share of expenses. In the case of a car accident, typically the auto insurance will be primary and should pay medical expenses first. During the process of subrogation the health insurance provider will contact the auto insurance provider and negotiate who should pay the bills.
See http://en.wikipedia.org/wiki/Subrogation for additional information.