Utilities generally were monopolies, and most still are, except in the most deregulated areas. As asterion and OldGuy pointed out, they are considered “natural monopolies” in that the quantity of infrastructure necessary to deliver their stock in trade mitigates against having competing companies. Imagine if there were six competing electric companies, each with their own power lines running down your street!
To prevent abuse, most states have a Public Service Commission (names vary; the PSC is the most common usage) which theoretically regulates rates to permit the company to make a small profit for their stockholders while keeping the cost charged to the consumer as low as possible. The world not being ideal, the desires of the companies for more income tend to outweigh the desires of the consumers for lower rates, in many states.
Deregulation works in a variety of ways, ranging from turning the local utility company loose to charge what the market will bear to enforced competition. In its most extreme state, what happens is that you can choose to buy your electricity, gas, cable-TV, Internet, local phone, long distance phone, and other services from whatever company is willing to sell them to you, and that company will simply pay a fixed, standard rate to the company that owns the infrastructure servicing your home, to bring its service to you. Obviously, this works best with something like long distance telephone service, where the point of being connected to a network is basic and the actual ability to provide good service at low cost is the competitive factor. But I know of instances where the Podunk Power Co. sells power to the Smith home a few miles away, using the lines of Avaricious Edison, who formerly had a monopoly on service to the Smith home, and paying them to use their lines – but still able to sell its power at lower cost to them, while paying the line charge, than the rates Avaricious Edison was charging. (I didn’t coin that name idly!)
The public vs. private issue also plays a part here – most people get water and sewer service from their municipality, if they don’t have wells and/or septic systems of their own or shared with neighbors. But there are private water companies, and even private sewer-line companies (though these are fairly rare). Most people pay a utility company for electric service, but there are a number of areas where electricity is provided by a government-owned corporation, effectively at cost. Where natural gas is pumped to homes along gas lines as a public utility, it may be provided by the “power company” that also provides electricity, by a separate gas company, or again by a public-sector corporation.
Telephone service has become so complex in recent years as to not be worthwhile trying to summarize. Effectively in most areas one gets local service from a company with a franchise, while being able to select among a variety of long-distance companies, which generally include the company providing them local service. But I guarantee that if I said that as a generalization without adding this sentence, I would get up to 30 anecdotal posts telling me how telephone service conditions in Wartsburg, Ohio, or Frostbite Falls, Idaho, are quite different from what I said.
In general, cable TV still operates on the franchise system – a company agrees to provide certain basic services and opportunity to get others in exchange for the exclusive right to run coaxial cable carrying their services through a given area, that right being given by the municipality or county in the form of an exclusive franchise. And we won’t even think of discussing how one can access an ISP and what are available.