Immediately upon reading the Twiweekly challenge for government I saw the prompt; Any significantly advanced society will probably have government in one form or another. This made me ask, could an advanced society exist without a governing body? If not how advanced can a culture become before it requires a government?
There is a possibility for advanced culture without government: post-scarcity society.
Robotics and other technologies so advanced you can get almost any industrial product you need for free.
Population decreased so there is no limitation by resources. In fact, say that we mine/grow our resources in space so nobody has to see an ugly factory or mine entry from their houses.
Availability of goods leads to cultural changes, people no longer need to have the newest phone or the biggest car (because having it no longer represents success), public recognition is based in personal abilities (from writting good novels to producing the most imaginative cooking recipes). Also, violence is socially unaceptable.
Robots are available everywhere and can stop any altercation (say, someone who has drunk too much) before any actual damage happens.
No foreign threat (other countries).
If that sounds familiar, it is because it is pretty much like Asimov's Spacial worlds (they have some government, but then they were not isolated from other worlds).
@SJuan76's answer is excellent, but I think that post-scarcity is a little too soon to drop all government.
Violence is inherent in our genes. So while any citizen is able to do irreversible damage to another, we will still need police, a.k.a. government.
I think that a post-death society, where nanite surgery can repair any wound or even reverse death, maybe then we can stop trying to govern each other and get on with enjoying our (eternal) lives.
Any form of society at any level of development will generate some form of government. It's simply human nature to engage in politics and co-operation, and any group of people above two individuals will develop some form of government to self-regulate and administer their society.
Post-scarcity doesn't mean anarchy, it just means most injustices can be eliminated, if the political will to do so exists in your society. However, there is virtually no human activity which is not impacted in some way by government, so the study of government is also the study of culture, philosophy and anthropology.
The only way to be truly free of government is to live completely alone in an isolated area where there is no chance that your activity can impact others or the activity of others can impact you.