Then there is that deductible
A deductible is the amount of money you will have to pay for any kind of damages before the insurance company kicks in the rest. They were implemented to keep small and non-legitimate claims from ballooning insurance company costs. The higher the deductible you are willing to put up with "in case", the lower your premium will be.
Collision and comprehensive insurance and sometimes medical and PIP coverage will have deductibles. Set your deductible as high as you can, as you will save big time in premiums, particularly in the liability coverage.