Most people are peaceful and want to interact voluntarily. For those who do not, there would be common law courts made up of local volunteers. Those volunteers would not have double standards under the law that granted them powers others did not, and they would not have special protections like current agents of the state enjoy. If you did not abide by the rulings of those courts, you'd lose protection from them. For larger issues? There would be the militia as defined in the Virginia Declaration of Rights--written well before the US Constitution and the Bill of Rights:
Section 13. That a well-regulated militia, composed of the body of the people, trained to arms, is the proper, natural, and safe defense of a free state; that standing armies, in time of peace, should be avoided as dangerous to liberty; and that in all cases the military should be under strict subordination to, and governed by, the civil power.