The only connection that the federal government has to car insurance is that it limits the amount of federal highway assistance provided to states that do require insurance under state law. While this is not a direct requirement for people to have insurance, the funds provided for highway projects is a tremendous incentive that most of the states have chosen to accept.
Today, car insurance of some sort is required throughout the United States. Typically, the requirement is for a minimal amount of bodily injury and property damage liability, although a few states currently use the PIP insurance model instead. Failure to carry the state required minimum will result in the suspension of your license or vehicle registration, and may entail carrying additional coverage or SR-22 Proof of Financial responsibility.
In most states, you can choose not to carry insurance if you are willing to deposit a specific amount with your state DMV or Department of insurance. The amount of this bond varies from one state to another, but is usually in the range of 50 to 100 thousand. Some states will also allow you to purchase such a bond from independent agents, including banks.
The minimum insurance required by state law should not be considered the best coverage to have. Such policies typically provide lower coverage amounts than a serious accident might require, increasing the chance that you will face large out of pocket costs in addition to what the insurance pays. Before buying any car insurance policy, make sure that the limits and deductibles of the policy meet your own personal and financial needs.
There are also optional auto insurance policies available, and some of them are required by dealerships. If you have a car loan, you may be required to carry full coverage, for example, which includes both collision and comprehensive insurance plans. Some dealerships will also require GAP insurance which will cover the difference between your car loan balance and the value of the car if it becomes totaled.