Rocks sent a link to this fascinating article on private law creation and enforcement in 10th-12th century Iceland:
I have described the legislative and judicial branches of "government" but have omitted the executive. So did the Icelanders. The function of the courts was to deliver verdicts on cases brought to them. That done, the court was finished. If the verdict went against the defendant, it was up to him to pay the assigned punishment--almost always a fine. If he did not, the plaintiff could go to court again and have the defendant declared an outlaw. The killer of an outlaw could not himself be prosecuted for the act; in addition, anyone who gave shelter to an outlaw could be prosecuted for doing so.

Prosecution was up to the victim (or his survivors). If they and the offender agreed on a settlement, the matter was settled.
Killing was made up for by a fine. For murder a man could be outlawed, even if he was willing to pay a fine instead. In our system, the difference between murder and killing (manslaughter) depends on intent; for the Icelanders it depended on something more easily judged. After killing a man, one was obliged to announce the fact immediately; as one law code puts it: "The slayer shall not ride past any three houses, on the day he committed the deed, without avowing the deed, unless the kinsmen of the slain man, or enemies of the slayer lived there, who would put his life in danger." A man who tried to hide the body, or otherwise conceal his responsibility, was guilty of murder.
One obvious objection to a system of private enforcement is that the poor (or weak) would be defenseless. The Icelandic system dealt with this problem by giving the victim a property right--the right to be reimbursed by the criminal--and making that right transferable. The victim could turn over his case to someone else, either gratis or in return for a consideration. A man who did not have sufficient resources to prosecute a case or enforce a verdict could sell it to another who did and who expected to make a profit in both money and reputation by winning the case and collecting the fine. This meant that an attack on even the poorest victim could lead to eventual punishment.

A second objection is that the rich (or powerful) could commit crimes with impunity, since nobody would be able to enforce judgment against them. Where power is sufficiently concentrated this might be true; this was one of the problems which led to the eventual breakdown of the Icelandic legal system in the thirteenth century. But so long as power was reasonably dispersed, as it seems to have been for the first two centuries after the system was established, this was a less serious problem. A man who refused to pay his fines was outlawed and would probably not be supported by as many of his friends as the plaintiff seeking to enforce judgment, since in case of violent conflict his defenders would find themselves legally in the wrong. If the lawbreaker defended himself by force, every injury inflicted on the partisans of the other side would result in another suit, and every refusal to pay another fine would pull more people into the coalition against him.