Liability coverage is offered for bodily injury (BI) or property damage (PD) for which the insured driver is deemed responsible. The amount of coverage provided (a fixed dollar amount) will vary from jurisdiction to jurisdiction. Whatever the minimum, the insured can usually increase the coverage (prior to a loss) for an additional charge.
An example of Property Damage is where an insured driver (or 1st party) drives into a telephone pole and damages the pole, liability coverage pays for the damage to the pole. In this example, the drivers insured may also become liable for other expenses related to damaging the telephone pole, such as loss of service claims (by the telephone company), depending on the jurisdiction. An example of Bodily Injury is where an insured driver causes bodily harm to a third party and the insured driver is deemed responsible for the injuries. However, in some jurisdictions, the third party would first exhaust coverage for accident benefits through their own insurer (assuming they have one) and/or would have to meet a legal definition of severe impairment to have the right to claim (or sue) under the insured driver's (or 1st Party's) policy. In some jurisdictions: Liability coverage is available either as a combined single limit policy, or as a split limit policy:
Combined single limit
A combined single limit combines property damage liability coverage and bodily injury coverage under one single combined limit. For example, an insured driver with a combine single liability limit strikes another vehicle and injures the driver and the passenger. Payments for the damages to the other driver's car, as well as payments for injury claims for the driver and passenger, would be paid out under this same coverage.
A split limit liability coverage policy splits the coverages into property damage coverage and bodily injury coverage. In the example given above, payments for the other driver's vehicle would be paid out under property damage coverage, and payments for the injuries would be paid out under bodily injury coverage. Bodily injury liability coverage is also usually split as well into a maximum payment per person and a maximum payment per accident. In the state of Oklahoma, you must carry at least state minimum liability limits of $25,000/50,000/25,000. If an insured driver hits a car full of people and is found by the insurance company to be liable, the insurance company will pay $25,000 of one persons medical bills but will not exceed 50,000 for other people injured in the accident. The insurance company will pay property damage not to exceed 25,000 in repairs to the vehicle that the insured hit. In the state of Indiana, the minimum liability limits are $25,000/$50,000/$10,000 so, there is a greater property damage exposure for only carrying the minimum limits.
Full coverage is the name commonly referred to as Comprehensive and Collision. Insurers generally do not use this term because it implies broader coverage than actually exists.  Collision Collision coverage provides coverage for an insured's vehicle that is involved in an accident, subject to a deductible. This coverage is designed to provide payments to repair the damaged vehicle, or payment of the cash value of the vehicle if it is not repairable. Collision coverage is optional, however if you plan on financing a car or taking a car loan, the lender will usually insist you carry collision for the finance term or until your car is paid off. Collision Damage Waiver (CDW) or Loss Damage Waiver (LDW) is the term used by rental car companies for collision coverage.
Comprehensive (a.k.a. - Other Than Collision) coverage provides coverage, subject to a deductible, for an insured's vehicle that is damaged by incidents that are not considered Collisions. For example, fire, theft (or attempted theft), vandalism, weather, or impacts with animals are types of Comprehensive losses.
Uninsured/underinsured Motorist coverage
Underinsured coverage, also known as UM/UIM, provides coverage if an at-fault party either does not have insurance, or does not have enough insurance. In effect, your insurance company pays your medical bills, then would subrogate from the at fault party. This coverage is often over looked and very important. In Colorado for example, it was estimated in 2007 that 24% of drivers did not carry the state minimum liability limits required by law. That is about 1 out of every 4 drivers. Unfortunately, this number goes up significantly during recessions. In some area's it is estimated that 1 out of every 3 drivers don;t carry insurance. Usually your limits match your liability limits. Some insurance companies do offer um/uim in an umbrella policy. In the United States, the definition of an uninsured/underinsured motorist, and corresponding coverages, are set by state laws.
Loss of use
Loss of use coverage, also known as rental coverage, provides reimbursement for rental expenses associated with having an insured vehicle repaired due to a covered loss.
Loan/lease payoff coverage, also known as GAP coverage or GAP insurance, was established in the early 1980s to provide protection to consumers based upon buying and market trends.
Due to the sharp decline in value immediately following purchase, there is generally a period in which the amount owed on the car loan exceeds the value of the vehicle, which is called "upside-down" or negative equity. Thus, if the vehicle is damaged beyond economical repair at this point, the owner will still owe potentially thousands of dollars on the loan. The escalating price of cars, longer-term auto loans, and the increasing popularity of leasing gave birth to GAP protection. GAP waivers provide protection for consumers when a "gap" exists between the actual value of their vehicle and the amount of money owed to the bank or leasing company. In many instances, this insurance will also pay the deductible on the primary insurance policy. These policies are often offered at the auto dealership as a comparatively low cost add on that can be put into the car loan which provides coverage for the duration of the loan.
GAP insurance is needed if you expect to owe more on the car loan than the car is worth (referred to as being “upside down”). This can occur if you are not able to afford a large down payment and you buy a car that depreciates rapidly, if you are paying a high interest rate, and/or if you are rolling some other expenses into the car loan, like money owed on a trade-in. GAP insurance is also common when leasing a vehicle as leasers are still responsible for the car if it is totaled or stolen just as if they had purchased it. 
Consumers should be aware that a few states, including New York, require lenders of leased cars to include GAP insurance within the cost of the lease itself. This means that the monthly price quoted by the dealer must include GAP insurance, whether it is delineated or not. Nevertheless, unscrupulous dealers sometimes prey on unsuspecting individuals by offering them GAP insurance at an additional price, on top of the monthly payment, without mentioning the State's requirements.
In addition, some vendors and insurance companies offer what is called "Total Loss Coverage." This is similar to ordinary GAP insurance but differs in that instead of paying off the negative equity on a vehicle that is a total loss, the policy provides a certain amount, usually up to $5000, toward the purchase or lease of a new vehicle. Thus, to some extent the distinction makes no difference, i.e., in either case the owner receives a certain sum of money. However, in choosing which type of policy to purchase, the owner should consider whether, in case of a total loss, it is more advantageous for him or her to have the policy pay off the negative equity or provide a down payment on a new vehicle.
For example, assuming a total loss of a vehicle valued at $15,000, but on which the owner owes $20,000, is the "gap" of $5000. If the owner has traditional GAP coverage, the "gap" will be wiped out and he or she may purchase or lease another vehicle or choose not to. If the owner has "Total Loss Coverage," he or she will have to personally cover the "gap" of $5000, and then receive $5000 toward the purchase or lease of a new vehicle, thereby either reducing monthly payments, in the case of financing or leasing, or the total purchase price in the case of outright purchasing. So the decision on which type of policy to purchase will, in most instances, be informed by whether the owner can pay off the negative equity in case of a total loss and/or whether he or she will definitively purchase a replacement vehicle.
Car towing coverage is also known as Roadside Assistance coverage. Traditionally, automobile insurance companies have agreed to only pay for the cost of a tow that is related to an accident that is covered under the automobile policy of insurance. This had left a gap in coverage for tows that are related to mechanical breakdowns, flat tires and gas outages. To fill that void, insurance companies started to offer the car towing coverage, which pays for non-accident related tows.
Personal items in a vehicle that are damaged due to an accident would not be a covered under the auto policy. Any type of property that is not attached to the vehicle should be claimed under a homeowners or renters policy.