Here is an article by Brigid over at Home on the Range, which lays out the reality of broad ownership of firearms in the old west. Her article clearly dispels many of the untrue myths that have been created by Hollywood, and also by the gun-control people who want to put guns in a bad light.
It is an excellent article, please read it. But in short, because people generally had guns and knew how to use them, violent crime of all sorts was far less than it is today. And people were more polite back then, too.