Anarchist!? I've never heard it called Anarchist before. I suppose that is a reasonable description of the pathological final years of the Commonwealth, but earlier?
There were regular meaning of the Quarter things (I forget what schedule), and ?annual? meetings of the Althing. In between the godhar (chieftains) had some authority. And there was always the more informal methods - like feuding. But even feuds were judged at the Things, and Wergild and banishment were applied for balance.
A modern bureaucratized society, no! a peace and light democracy? (well, no, but I won't admit I said that) Anarchy? Hardly!
Yes, well calling the Icelandic commonwealth an anarchy is not very helpful to explain what it was.
Basicly, there were lots of "Things" (þing), of which all were regional except for Althingi which was sort of considered the supreme court.
In reality that was what the Things were, they were used for legal purposes like courtrooms, with some trading, socializing and some marriage arranging.
The laws of the Things were not under discussion, or at least very rarely. They were based on traditions reaching from ancient norway and even further maybe. Probably most german nations had a thing tradition but the evidence is rather scarce so it remains a hypothetical theory.
In any case you could well have a Thing and still have a king that collected taxes. For the king was not per say an authority in german societies for making juridicial calls.
Iceland might be called anarchy in the sense that it had no central government. But this is not anarchy in some anarchocapitalist or anarchosyndicalist sense. For example one can also point out that women could divorce, own and be considerably freer than women in Italy or Syria at the time. Yet it is not a feminist state.
The Gothis (goðar) were high priests and usually the biggest land owner. Their authority was somewhat dependent on the land they owned, other free man could choose between their Godis which took the role of their lawyers and protectors. They didn´t really gather tithes until they became responsible for churches as well. The churches needed taxes to keep going and that´s where the trouble begins.
Prechristian Iceland is not an ideal society in any sense though. Rampant violence and feuds posed problems, and noone really had the authority to deal with it. Althingi could conclude that someone should be outlawed or killed, however in a lots of cases noone was strong enough to enforce the resolutions. (Sort of like the UN in many cases

).
Also noone gave a rat´s ass about slaves, and if you were homeless or without a family you could be easily killed without any repercussions.
This situation ended during the 12th century when the Godis became powerful enough to deal with all lawbreakers. Unless the Godi himself was a lawbreaker of course. Some sagas tell about how some powerful Godis abused their situation and basicly mistreated people in their area without any man willing or powerful enough to stand up against them.
///This lecture is not pointed at Dathi, but more at everyone in general, I hope my rant

was informative///