In the United States, insurance is regulated by the states under the McCarran-Ferguson Act, with "periodic proposals for federal intervention", and a nonprofit coalition of state insurance agencies called the National Association of Insurance Commissioners works to harmonize the country's different laws and regulations. The National Conference of Insurance Legislators (NCOIL) also works to harmonize the different state laws.
Liability insurance is a very broad superset that covers legal claims against the insured. Many types of insurance include an aspect of liability coverage. For example, a homeowner's insurance policy will normally include liability coverage which protects the insured in the event of a claim brought by someone who slips and falls on the property; automobile insurance also includes an aspect of liability insurance that indemnifies against the harm that a crashing car can cause to others' lives, health, or property. The protection offered by a liability insurance policy is twofold: a legal defense in the event of a lawsuit commenced against the policyholder and indemnification (payment on behalf of the insured) with respect to a settlement or court verdict. Liability policies typically cover only the negligence of the insured, and will not apply to results of wilful or intentional acts by the insured.
Formal self-insurance is the deliberate decision to pay for otherwise insurable losses out of one's own money. This can be done on a formal basis by establishing a separate fund into which funds are deposited on a periodic basis, or by simply forgoing the purchase of available insurance and paying out-of-pocket. Self-insurance is usually used to pay for high-frequency, low-severity losses. Such losses, if covered by conventional insurance, mean having to pay a premium that includes loadings for the company's general expenses, cost of putting the policy on the books, acquisition expenses, premium taxes, and contingencies. While this is true for all insurance, for small, frequent losses the transaction costs may exceed the benefit of volatility reduction that insurance otherwise affords.
The cheapest car insurance, period, will likely carry the minimum coverage required in your state. In most states, this is liability insurance only, which covers property damage and medical bills for others due to accidents you cause. Some states also require uninsured and underinsured motorist coverage, which pay for your injuries or damage if an at-fault driver doesn’t have enough insurance.