I would like to add that there are legal monopolies. Natural monopolies exist because it would be economically inefficient to force more than one company into certain markets and industries. The start-up costs are too high, customer base is limited, or profit margins are too small. In these instances, regulatory agencies fix prices to prevent companies from taking advantage of customers.
The monopolies do not mind the extra regulation because they enjoy the lack of competition, and competition does not force them into a situation where they must constantly spend revenue on making technological improvements. In industries with natural monopolies, technology is often mature, and maximum efficiency has been reached (arguably). The most common natural monopoly is a utility.