Even for those who are not anarchists, it is useful to know the points at which government tends to malfunction and harm the general populace. I've been thinking a lot about that, and collecting references for my own purpose.
As far as I can tell, there seems to be three core problems from which many others derives:
1. The problem of limited knowledge, and making decisions that affect masses of people based on it.
2. The problem of power attracting the people who abuse it.
3. The problem of interring Official Authorization upon incompetent people.
4. The problem of blind righteousness given considerable power.
All of those are problems that exist more or less anywhere (for example the third exists in any bureaucracy), but governments have more power than most group-entities to affect others with their mistakes, and inherently feel authorized, even mandated, to exercise their power.( Expanded Examples. )
4. Blind righteousness with power. For an extreme example of this, it's easy just to look at theocracies, but this extends into countless things. I've seen nasty righteousness from all political stripes including 'apolitical'. (I've only just now edited this in, so I'll find an example for you people later. I'm sure you can readily exercise your own minds to find some, however.)
I think those problems are important considerations even for people who still hold faith for a sufficiently well-managed government to accomplish much good. I see a lot of "the government should handle, government should do this or that" this in response to problems, without much consideration of how to rein in government abuse and mismanagement of the response.