Adam Smith: Withering away of the state? Private profit-making rights-enforcement organizations? Have none of you ever taken a trip to the Scottish Highlands? Have none of you ever read about the form of society that used to exist there? In the Scottish Highlands David Friedman's dream of a society without a state, in which justice was administered by private profit-making rights-enforcement organizations, was a reality. And what a reality! The private profit-making rights-enforcement organizations were called "clan lords" and their henchmen. In the Highlands, everyone was seen as either a clan member to be helped, a clan enemy to be killed, or a stranger to be robbed. With such insecurity of life and property, the system of natural liberty could not operate to create prosperity, and life was... what is the phrase?...
Thomas Hobbes: Nasty, brutish, and short.and
Davey Hume: Exactly. That is the key problem of governance: mighty, but limited. It is only after the state has been established and the memory of what life was like in the Highlands disappears that people can even begin to forget why the state is necessary. Under security of property, people begin to view each other--even total strangers--as possible partners in mutually-beneficial acts of exchange. The oxytocin levels in their bloodstreams rise. They feel mutual sympathy toward each other. They feel bound by the moral law, and no longer kill clan enemies or rob strangers even when they can do so in perfect safety...I think that this sort of problem of fading memory is common. The regulations that make fires less likely (or that establish fire departments) seem less useful in a world in which they are highly effective and so we don't see the day to day need for the intervention.
A good medical example is vaccination. At one time people were (correctly) terrified of these diseases and the death, disability, or disfigurement that they could cause. In a world where there are a lot of measles vaccinations being given (and where we have all forgotten the polio/smallpox/measles epidemics) it can be easy to ask the question: "why do we subject our children to the risks of being vaccinated" (given that these risks may not be zero). Of course, when vaccination stops, the same diseases may quickly come back. And, even so, it might not be easy to get all children vaccinated because the consequences are not fully realized until it is way too late.
In the absence of a state, I don't really see a clear solution to the free rider problem. Even enforcement of damages presumes somebody (i.e. a state actor) to enforce the claim to damages (or a rather brutal enforcement process at the point of a gun). Since people may forget just how bad the previous era really was, it can be hard to prevent things from deteriorating.
But it isn't a problem just limited to the state, itself, but it shows up in many successful areas of human intervention where the intervention is a victim of it's own success.
Mark added as a private comment that this can be extend to a lot of different areas. He gave the examples of bedbugs and economic insecurity, both of which are on the rise because we don't have the urgency of prevention that we used to have.