Natural Monopoly: The most common example of a natural monopoly is water. It would not be practical to create a competitive market for water because of all the necessities that come with owning a water company. It would cost way more money to install pipes running to individual costumers and such than the company would make.
Government Monopoly: The United State Postal Service is prime example of government monopoly. No other company ships first and third class mail, they are not allowed to. Although other companies compete in shipping packages or overnight delivery, good old "snail mail" is a government monopoly.
Geographic Monopoly: A geographic monopoly example is a small town store in Northern Alaska with no other stores around to compete. In Alaska, shopping malls are not popular so many times there is just a single store every hundred miles or so to buy everything you need.
Technological Monopoly: The John Deere plow is an example of a technological monopoly because John Deere has a patent on it. He advanced the world of farming through technology and received his credit through a patent.