Even though it is the law in most states and provinces to have a minimum amount of liability insurance, there are many people on the road that can not afford, or simply do not have insurance. The main reason that motorists choose to drive without insurance, is that they want to save money or can not afford to pay the premiums.
Liability coverage covers injuries to third parties, which result from accidents for which you are at fault. If you are found to be at fault for an accident, you are liable for all damages that you cause to others. These damages include both bodily injury and property damage, and could end up being several thousands of dollars! Without liability insurance, the injured parties could sue you for pain and suffering, medical expenses and property damage, which could cost you much more. It is a much smarter idea to pay the premiums and get liability coverage.
If you are involved in an accident which you are not at fault, and do not have insurance, the at-fault rules still apply. You will be still covered by the other motorist's liability coverage, for your injuries and damages. Being compensated for injuries that were caused by other motorists has nothing to do with whether or not you have insurance. Of course you may be charged with driving without insurance and forced to face the penalties associated with that charge in your state or province.
If you have insurance and were in an accident with an uninsured motorist who was at fault, this can be a real headache, unless you have uninsured motorist insurance. If you have un-insured motorist insurance, then your insurance company will cover you up to your limit that you set for uninsured motorist insurance. The insurance company would then sue the uninsured motorist to collect for their damages. If you do not have uninsured motorist insurance, it would be fully up to you to collect for damages. You would have to sue the uninsured motorists, and invest the time and money to do so. An important thing to remember is that even when you win the lawsuit, no payment is guaranteed. If they could not afford auto insurance in the first place, how are they going to afford paying for your medical bills? This is the reason that selecting un-insured motorist insurance is a wise decision. You are covered for your losses immediately and the insurance company deals with the hassle of the lawsuit.
In close driving without insurance is not a good idea. In the long term, the small yearly premium for auto insurance will protect you from the large bills, or possible wage garnishments that may be applied if you are at fault for an accident. Un-insured motorist insurance is a wise addition to anyone's coverage to avoid the headache that can arise from an accident involving an uninsured motorist.
Remember that the information presented above is general information, and each state / province has different laws dealing with insurance. Also each auto insurance company and policy is different, so it is best to check with your company to see exactly what your policy covers.