Most states require car insurance because expenses can get very high quickly if you are in an automobile accident. Liability is normally the minimum requirement, which pays for damages caused by your vehicle. The major other types of insurance cover you car and medical expenses related to accidents. Some states allow you to post a bond instead of paying insurance, and of course some people break the law and drive without insurance anyway.
Here is a breakdown of the basic types of automobile insurance
Liability
Liability is the basic coverage required. This covers damages to other people's vehicles if you are at fault in an accident. Liability insurance should also cover injuries suffered by people in the accident. Property damage can also be a part of this as you could damage something other than someone's car. You may purchase insurance at various limits, and as you go up the price increases.
Collision
This is usually not required and it covers your own vehicle when you are in an accident. The value of your car, and whether you owe against it, are prime considerations. Most loan companies require you to have this kind of insurance. Collision will cover your car if you run into another car, run into an object, or roll the vehicle over. Pay attention to the details of your policy, as many insurers cover only the fair market value of the vehicle, and have the option of deciding whether to declare it a total loss. For instance, if your car will need $5,000 in repair, but is worth only $4,000, the insurance company will give you the $4,000 instead of repairing it. You can get replacement insurance which is slightly different.
Comprehensive
Comprehensive insurance is sort of an "everything else" type policy. This covers your car if it is stolen or vandalized, or if it is in a fire. Things falling from the air, like rocks from a hillside, or hitting an animal on the road, would be covered by a comprehensive policy. Glass repair is sometimes included, and sometimes not, so it is a good idea to make sure you know exactly what is covered.
Uninsured motorist
While insurance is required, not everyone obeys the law, and this will cover you if you happen to get into an accident with someone who is not insured. It can also protect you if there are major damages and the other driver has minimal coverage that will not fix all your damages.
The rest
There are many other smaller types of insurance, or add-ons, that you can get related to car insurance. There is "gap" insurance that will cover you if you owe more on your car than it is worth. This will cover the difference. If your car is totalled, the loan company still has to be paid.
Policies for roadside assistance are also sort of a car insurance, as they get you aid if your car breaks down. You may also get insurance for when you will be renting a car, as opposed to getting it from the rental agency. There are also theft policies available to cover you if something is stolen from your vehicle.