I have been reading up on the Amish for one chapter of the book on legal systems very different from ours that I'm currently working on. They provide an example of what I think of as an embedded legal system—a group that is under the authority of an external legal system, but also has its own legal system which it succeeds in enforcing on its members. Other examples are modern gypsies and Jewish communities during the diaspora, which were often given the right to impose Jewish law on their members by their gentile rulers.
It occurred to me that one could view the Amish as a working example of a form of anarchy. It is a very strange form, since the rules that the Amish are under are considerably more constraining—including rules on what styles of clothing they can wear, rules against owning automobiles or flying on airplanes, and much else—than the rules the rest of us are under. But those rules are all voluntarily accepted, and the system that generates them may reasonably be viewed as a competitive system of private law.
To expand on that, for readers not familiar with the Amish... . The only level of Amish "government" with any authority is the congregation, typically made up of about thirty to forty households. Its authority is over individuals who, as adults, have chosen to swear to accept its rules. The only punishment it can impose is shunning—the refusal of members of the congregation to associate in various ways with a member who has been excommunicated. Members, including excommunicated members, are free to resign from their congregation and join any other congregation that will accept them, or drop out of the Amish sect entirely.
The rules—the ordnung—vary from one congregation to another and change over time. In some settlements the congregations are, in effect, miniature territorial sovereigns, so if a member of one congregation wants to shift to another, perhaps because its rules are less (or more) strict than the rules of his current congregation, he has to physically move, although often not very far. In other settlements, especially ones where there are congregations with a considerable range of different versions of the Ordnung, congregations overlap, so you can switch congregations while remaining in the same location.
It's true, of course, that the Amish are under the rule of the U.S. (or, for a smaller number, Canadian) government. But they receive very few services from government, since they are unwilling to accept most of the conventional forms of government aid and, as pacifists, are unwilling to report crimes against themselves to the police or sue in the government courts to collect debts. Off hand, the only significant benefit I can think of that they get is protection against foreign invasion. And, on the other hand, governments at various levels imposes sizable costs on them, in the form of taxes that (with the exception of Social Security) they have to pay and regulations.
So I think they provide pretty good evidence of at least one form of (very structured) anarchy that works.