Is it better for the economy if the government steps in and regulates monopolies, or will monopolies work themselves out if left alone?
As for the monopolies that consumers do not like, they historically work themselves out, so long as government stays out of the way. If monopolists are making large profit margins, other entrepreneurs with capital they are looking to put in another venture will see those margins and want a slice of the pie. This increases competition in that market, removing the monopoly, and benefiting the consumer.
However, there are many examples of governments protecting monopolies. My favorite example to go to are patents. Patent (and other intellectual property laws) are created to give the creator a monopoly on the design of their product.