Anarchy doesn't exist, it's not real, infact it probably would take more effort to stustain an anarchy than any other government.
You may be able to get rid of formal governmental leaders, but leaders will crop up who organize projects that people need. You might be illusioned with the idea that the government is nothing more than the president and congress that goes around raising the price of oil and waging wars.
1) Every Municiple resource given to you is spearheaded by the government.
2) Construction projects, Fixing roads, buildings, improving communities, infrastructure, even if this was done by a private buisness, the private buisness needs a leader, since this private buisness does things for the community [Technically] they become the government, even if you don't consider it to be one.
3) Police forces do more than just beat up old people, tazer them, and kill them. When a Traffic light breaks down, who's going to dirrect traffic? you?
If you Fall and injure yourself, who's going to come to your aid, even if you have family members, how many of them are trained in emergency medicine? If somone robs a bank?
All of these things could be done by private buisnesses, but consider the fact that whoever leads these organizations is number 1, probably going to have to do it for profit since they can't collect money in taxes, and number 2, they ARE THE GOVERNMENT they control affairs in society.
I have to go to sleep, but you get the idea.
You need a government, you can make it small or big, autocratic or inneificiently decentralized, usually the more efficient governments win out the same way the strongest and most efficient specie survives, but either way, the government does things that can't be done by individuals, only by a group of people.
if you want anarchy, then live somewhere on the countryside and set up an independent farm where you can support yourself and your family, that's as close to anarchy as you'll get. But since you run your own affairs, you become your own government.