A form of society based around the lack of a ruling class and an emphasis on individual freedom and equality. An ideal form of anarchy would involve a cooperative socialist gift economy, in which goods are freely produced and distributed according to need. Crime would not be the huge problem most people would imagine. Anyone with a basic knowledge of history knows that crime was never a huge problem until urbanization and then industrialization. A focus on community and civic responsibility would nearly eliminate violent crime (smaller, tightly knit communities have virtually no crime, even today). Property crime would be even a less of a problem, given that no one has more than anyone else and destruction of public property would be destruction of one's own property. In case a crime is committed, any and every member of the community is capable of either preventing the crime before hand or apprehending the criminal afterwards, a system which worked for thousands of years before police forces became common during the Industrial Revolution. A common argument against such a system is that "human nature" would eventually lead to a return of capitalism and the establishment of government. This is not a part of "human nature", however. Human beings have almost no instincts at birth. A tendency towards government and capitalism is a product of societal conditioning, not a natural inclination. There have been examples of similar systems working in the real world, including many in Spain during the Revolutions of the late 1930's. Living standards generally increased in these areas.
"I had dropped more or less by chance into the only community of any size in Western Europe where political consciousness and disbelief in capitalism were more normal than their opposites. Up here in Aragon one was among tens of thousands of people, mainly though not entirely of working-class origin, all living at the same level and mingling on terms of equality. In theory it was perfect equality, and even in practice it was not far from it. There is a sense in which it would be true to say that one was experiencing a foretaste of Socialism, by which I mean that the prevailing mental atmosphere was that of Socialism. Many of the normal motives of civilized life--snobbishness, money-grubbing, fear of the boss, etc.--had simply ceased to exist. The ordinary class-division of society had disappeared to an extent that is almost unthinkable in the money-tainted air of England; there was no one there except the peasants and ourselves, and no one owned anyone else as his master." -George Orwell, on an anarchist community in Spain during the Revolution