The biggest problem that neither anarcho-socialists (what we traditionally mean by the word "anarchists") or anarcho-capitalists (a.k.a. "Libertarians", "glibertarians", "libertards") have an answer to is the free loader problem. And without an answer to the freeloader problem, they are condemning their white pasty flabby asses to become some sociopath's bitch if they ever got their anarchist's paradise that they wish for.
So how does this happen? Well, consider the problem of sociopaths in general. There are two kinds of people -- regular people, who hesitate at the taking of life, and sociopaths, who enjoy taking lives. In a gunfight between a sociopath and a regular person, the sociopath wins, because he who hesitates loses in a gunfight. So in a no-government Libertopia, sociopaths will swiftly kill the most courageous of the regular people, those who try to take them on, and the rest of the regular people will get the message that they're the sociopath's bitches and quit trying. See: Somalia, Afghanistan, the inner city of most U.S. cities, the state prison system of most U.S. states...
Now I hear you saying, but in Libertopia we'll have private cops to take the sociopaths off and put them away! But: Who is going to pay for these private cops? If Bill Gates pays for the private cops, everybody else is freeloading off of Bill Gates! Unless *everybody* pays for getting Jeffrey Dahmer off the streets, the end result is that NOBODY pays, because Bill Gates isn't going to pay when it's just going to benefit the families of the people actually killed by Jeffrey Dahmer! Instead, he's going to retreat behind his own fences and go out with his own armed guards, and leave Jeffrey Dahmer out there to meet other Jeffrey Dahmers at which point you now have an army of Jeffrey Dahmers who are raping, pillaging, and cannibalizing at will because ordinary people who dare try to take a shot at them get killed because, well, they hesitate.
The reality is that the only way to keep this army of Jeffrey Dahmers from forming is for everybody to pay for the trained cops and prison system to keep them off the streets (or at least on the payroll so that they're going after other Jeffrey Dahmers rather than cannibalizing the people as a whole). I.e., taxes, enforced by government. Which the glibertarians and anarchists don't believe in, in their heart of hearts, chanting "taxation is theft!" and shit like that.
But for some reason the glibertarians and anarchists don't see it that way, the glibertarians claiming that ordinary people with ordinary weapons have any chance at all against sociopaths (they don't, he who hesitates loses in a gunfight and ordinary people simply do not like violence and killing and thus aren't good at it unless they get a lot of training paid for by, err, government), and the anarchists simply handwaving the problem away and claiming that their voluntary syndics will work sufficiently well for self defense and sociopaths won't be able to take them over and force the members to their bitches (hah!). It is to laugh, really, at just how divorced from reality these people are. Mao had it right: Power flows from the barrel of a gun. And sociopaths are damned good at using guns due to their complete lack of morals and scruples... giving them much more power than their numbers would indicate they should have. Without a solution to the freeloader problem, there's simply no way to pay for the large number of ordinary people needed to keep sociopaths down -- and the glibertarians and anarchists (and the rest of us, alas) end up as the sociopaths' bitches.
-- Badtux the non-freeloader Penguin