If we include small scale societies, we get more radical egalitarian examples. Marx (while knowing empirically very little about them) called such societies "primitive communism". Marshall Sahlins, one of my favorite anthropologists, wrote a ground-breaking article called "the Original Affluent Society" (a play on economist John Kenneth Galbraith book about the post-war US economy, the Affluent Society) in 1966. He argues, using examples like the !Kung in South Africa, that hunter-gather societies had more calories, more leisure time, more equality, etc. than neighboring agriculturalists. Basically, he argues that Hobbes' "state of nature" described in Leviathan where there's a war of "all against all" and man's life is "solitary, poor, nasty, brutish, and short" is just plain empirically wrong. Agriculture brings division of labor, and with that inequality. Read the whole article here (it's an easy read). His later book Stone Age Economics develops these ideas further. Jared Diamond (who is normally a whipping on this sub) has a great essay that was published in Discovery Magazine that develops on Sahlins' work called "The Worst Mistake in the History of the Human Race" (1987). Read it here. Some parts are a little dated, but makes the (I think correct) argument that agriculture dominated not because it was better for individual early agriculturalists but because it could provide more calories per acre, and therefore higher population density, and therefore the early agriculturalists could womp the local hunter-gathers when push came to shove. Because of this, the hunter-gather groups we see surviving into the modern period are generally on marginal land that agriculturalists simply don't want (the !Kung and others in the Kalahari Desert, a variety of groups in the Amazon Rainforest, aboriginal groups in Central Australia, etc.).

Pierre Clastres's Society Against the State (1974) is an enthography of the Guayaki. Most people haven't heard of this book, which is really too bad, because it's excellent. Calstres was supposed to be Levi-Strauss's intellectual heir, but he tragically died in a car accident three years after this book (based on graduate work) was published. He argues, in a way a bit different from Marx, Diamond, and Sahlins, that while these societies are not totally equal (they have a very clear idea of power) but take strong aims to limit this inequality--the chief, for example, is very, very limited in what he can do by society. This, he argues, gets you very close to anarchist society--it's not that no one has more power than the others, but that people work very actively to prevent the unnecessary accumulation of power (a chief is necessary, for example, in discussing matters with other tribes). You can read a long excerpt here. Clastres was influential on later anarchist anthropologists, particularly David Graeber and my personal hero James C. Scott. For anarchist anthropology, probably the best place to start is Graeber's Fragments of an Anarchist Anthropology (put out by Sahlins mini-press, Prickly Paradigm, which is maybe my favorite academic press). Being a good anarchist, the whole thing is available as a free PDF here and is worth reading. It was deeply influential on my thinking--my last year of undergraduate, we kept a print copy in our bathroom and we probably all read it three or four times in total. He like Clastres argues that it's not that small scale anarchist societies have no idea of power or exploitation or inequality, but that they see it daily (in how outsiders behave, in how men treat women, etc.) and therefore actively work to minimize it. They often have very active myths, charms, spiritual powers, etc. that they invoke to justify this equalizing. For example, in a case he cites from the Tiv who live in Central Africa:

Enterprising men who managed to patch together some sort of fame, wealth, or clientele were by definition witches. Their hearts were coated by a substance called tsav, which could only be augmented by the eating of human flesh. Most tried to avoid doing so, but a secret society of witches was said to exist which would slip bits of human flesh in their victims’ food, thus incurring a “flesh debt” and unnatural cravings that would eventually drive those affected to consume their entire families. This imaginary society of witches was seen as the invisible govern- ment of the country. Power was thus institutionalized evil, and every generation, a witch-finding movement would arise to expose the culprits, thus, effectively, destroying any emerging structures of authority.

Pretty cool, right?

James C. Scott emerged to fame by studying how people, especially peasants, resist power within states. If you've heard the terms "weapons of the weak" or "everyday resistance", you've heard of Scott's ideas. He argues that throughout history, peasant rebellions and insurrections are absolutely rare, but this doesn't mean that the rest of the time peasants consented to their conditions. Instead, we see hidden resistance in the form of: "foot-dragging, dissimulation, desertion, false compliance, pilfering, feigned ignorance and sabotage acts". Things like hiding grain from the tax collectors every year. He has a great article comparing this in pre-revolutionary France and 1970's Malaysia called "Resistance without protest and without organization: peasant opposition to the Islamic Zakat and the Christian Tithe" (1987), which you can read here. I think it's maybe the best introduction to his early work. In his middle work, through Seeing like A State, he turns his attention from the peasants to the state itself. Again, amazing, generative work about how the state does things like create last names in order to better tax and operate. You can read a popular summary of these ideas in his article for the libertarian Cato Institute "The Trouble with the View from Above" (every historian who works on states needs to read this). In his most recent period, really starting with The Art of Not Being Governed: An Anarchist History of Upland Southeast Asia and Three Cheers for Anarchism. He argues that these upland groups (the Hmong, the Shan, Kachis, etc) not only left the lowland, wet rice agriculture dominated states of Southeast Asia, but actively worked against being part of them--which worked until the states got rubber tires, all-weather asphalt roads, and helicopters, meaning that the autonomy of these groups has seriously declined since c. 1950. He argues that things like their agriculture was specifically designed to avoid exploitation. Cereals like wheat and rice have to be harvested all at once, so the tax man only has to show up with his army once around harvest time to get his cut. The Uplanders, however, avoided wet rice agriculture completely and instead relied on root crops that have to be dug up individually (meaning there are no granaries to tax), can stay fresh underground for two or three years, etc. and otherwise are just very hard for the state to get a cut of. He argues that the groups that had literacy actively left it behind (he realizes this is most contentious claim with the least empirical backing) in order so that they could rewrite kinship ties, history, etc. as contextually appropriate, rather than being locked into a single history. This let group X realize that they are "really brothers" of unrelated group Y when they needed to cooperate. Scott argues that society in general is organized along these anti-state lines, from language to myths to settlement structure to group size, etc. If you get your hands on a copy of the book, you can get the whole argument even just in the first chapter. If you have an hour free, you can watch a video lecture on this point here.

(cont'd)

The closest thing you will find is Catalonia in the 1930s during the Spanish Civil War, but it existed for a few short years, and the exigencies of war make it quite hard to study on its merits alone. I am not especially well read on the social organization, but I have written an answer before that touches on why, militarily at least, the Spanish anarchists, and other attempts at Anarchist societies, failed, which might interest you.

I would also suggest to you a few sources to look up.

"The Spanish Anarchists: The Heroic Years 1868-1936" by Bookchin and "No Gods No Masters: An Anthology Of Anarchism" edited by Guerin. The first looks at the development of Anarchism in Spain, although it doesn't really deal much with the Civil War period itself, while the latter is an excellent collection of writings on Anarchism, and includes a section on Spain which you would probably find enlightening.

Wouldn't most pre-colonial Native American tribes fall under that category?

1918 7 million people in the Free Territories of the Ukraine

1936 Catelonia Spain communes

1994 Chiapas Mexico EZLN

Some Pre-Civilization and Pre-Colonial tribes are considered anarchist