"Without the government, there would be no traffic laws and major accidents on every intersection."
— most statist fools
Watch this video and weep. On the left: traffic lights off during a power outage. On the right: back on, the next day (filmed at the same place, same time).
Or, in other words, left: libertarianism; right: statism.
This is not to suggest that we'd have no traffic laws in a stateless society. The point of the above video is that nothing is better than whatever the government has to offer and that "nothing" in most cases amounts to a spontaneous order due to the forces of mutual cooperation and pursuit of self-interest.
Under stateless society, all roads would be privately owned, and it would be up to the owner to create traffic laws and regulations (in the form of signs, traffic lights, etc.). Different road owners would compete with each other for the public's custom (passage through their roads, paid for automatically and electronically — price also kept low by competition). The competition would allow improvement in the quality of roads and traffic regulations (in terms of clarity, balance between safety and efficiency, etc.).
Another example, from England: