In my recent blue sky searching about Agorism, I came across a group in Detroit that is tackling the crime that plagues their city, going by the name Detroit Threat Management.
Of course, they don't describe themselves as Agorists, or, I'd imagine, Anarcho-Capitalists. But in a sense, they are a prototype Private Defence Agency, albeit one which focuses on stopping crimes in progress and operates under a higher court (incidentally, this is the closest we've come to proper Anarcho-Capitalism in history; from what I've heard about the Icelandic Commonwealth, the private police were responsibly only for enforcing the law, with a common court system above them). Interestingly enough, they don't limit themselves to the wealthy areas either, providing security for free to those who can't afford to pay for their services. In what might be the first example of Anarcho-Capitalism in action in modern America, we see a possible answer to the question of how the poor would get security (although the thinking rich might choose to provide it out of their own pocket anyway, since it would have the effect of reducing their own defence premiums by cutting off crime where it starts).
Getting back to the subject of Agorism, and counter-economic private law enforcement, the continued existence of the state places restrictions on how this can be done. However, there is nothing - at least, no law that I know of - that prevents individuals from stopping crimes in process (provided they use "reasonable force"). Indeed, volunteer groups like the Guardian Angels famously provide additional, non-state security in cities such as New York. Also, in the UK special constables are enabled to make arrests whether they are on or off duty, which raises the possibility that a group of special constables could form something of an enhanced neighbourhood watch patrolling their area (or, of course, just have one or two for making the actual arrests...).
My thoughts on Agorism and Real-life Superheroes are for another post...