The wild west is a great example of no government but a culture built upon self reliance and self defense. Being good with your gun was common, carrying guns was common. The wife and kids at home knowing how to shoot a rifle or shotgun was common. It was common for a reason. They also had the ability to raise a posse and organize spontaneously as people were more grounded and knew everyone in town, so going up against one person was going up against the whole town if you were being predatory.
In Iceland they had a great form of electing people to represent them in a competitive way and organize protection against other groups. It worked well until something more powerful, the Catholic church, came along and tipped the balance.
The absense of government will not necessarily create government but it will at least be replaced by people cooperating with one another in a way to best increase their ability to protect themselves. If everyone has equal power then the golden rule is a given, it is in both of their best interests to do so. With an unequal balance of power the one with the power gets to decide if the golden rule is followed, our US government has demonstrated that it does not need to follow that rule against those that are weaker.
But these were both in times where people accepted governments as being legitimate entities. The people were basically out on the frontier and accepted they didn't have their governments to look after them.
What if, the people had decided that the concept of the government was not legitimate? For example, what if the anarchists of today were able to convince enough people in the same way that people were eventually convinced that slavery was wrong or racism was wrong. While you will always have some people who think they are good ideas, the majority understand that they are not and the ideas become unacceptable in most of society. The government is fundamentally a much smaller group than the rest of society. If people were to decide tomorrow that they weren't going to pay their taxes I really don't imagine the government could do much. If it tried to make an example out of some people the rest would probably just break them out of jail or whatever needed to be done and eventually the government would run out of money to pay it's enforcers. If it was a foreign government invading an area I imagine it wouldn't go well in the same way that recent invasions of countries haven't gone well.
