Just like the abolitionists didn't particularly care about proving that economies could function without slavery by pointing at other societies that had already done so, I don't particularly care about proving that societies can function with limited or no government interference in people's lives. The morality of treating others respectfully using peaceful means as the self-owning, self-determining individuals they are is enough. As I quoted from Lew Rockwell, that doing so also unfetters human creativity and enabled very large increases in living standards pulling hundreds of millions of people out of extreme poverty to live far more meaningful and fulfilling lives is a happy happenstance.
However, reposting (yet again) this video of the 1,000 years that Ancient Ireland operated without Government (up until 17th century) is an example of a non-government system existed and lasted for numerous generations.
[youtube]http://www.youtube.com/watch?v=su9OqvBbSD0[/youtube]
Another example given by
David Friedman is saga period Iceland, while another given by
Anthony Caprio is the Republic of Cospaia (where "For nearly four hundred years, this tiny republic thrived in central Italy with no government, no rulers, no military, no bureaucracy, and no taxes.") For a long period of time the
American West operated very effectively with minimal or no government involvement (hint: it was nothing like most of the movies which are basically myths). There are also a range of others but, again, I - and probably nearly all other Libertarians - don't particularly care except from an academic point of view where it is interesting to learn about what institutions they used.