Each state has their own laws regarding driver and motor vehicle financial responsibility. Without the state, we cannot tell you when your state inacted laws requiring liability car insurance. While some state laws might require financial responsibility through an auto insurance liability policy, some states allow other ways for a person to carry FR on a vehicle, such as a bond held by the state. 

In most cases, drivers choose to obtain car insurance to comply with their state's FR law. When a car owner or driver chooses this option, there are general requirements set up by the state regarding the minimum amount of insurance one can purchase to satisfy the financial responsibility mandated by the state.

To find out when the insurance or FR law was passed in your state and the details of it, contact either your Department of Motor Vehicles or the consumer division of your state's insurance regulatory agency.

For example, Illinois required mandatory insurance as of January 1, 1990. 

Also, our article How Much Car Insurance Should You Buy gives a listing of state by state insurance requirements, which may help you understand your state's law better.