Burger King is a chain/franchisement of fast food restaurants spanning over 58 countries world-wide. It was founded in 1954 by partners James McLamore and David Edgerton in Miami, Florida under the original name of Burger King of Miami. The first location was at 3090 NW 36th Street in Miami and served the national standard hamburger.
In 1957 Burger King introduced their cash cow (pun intended), the Whopper Sandwich (at the staggering price of 37 cents) and it immediately became the company's largest selling item.
The company expanded and franchised itself over the next decades and in 1967 Pillsbury bought the company and all 274 locations for $18 million and soon after the "Have it your way" slogan was introduced. Salad Bars were introduced into the stores in 1983 and then quietly extinguished a few years later, around the time they introduced the Croissan'wich in 1985. In '88, Grand Metropolitan PLC acquires The Pillsbury Company and its subsidiaries, including Burger King Corporation, for $5.79 billion. Grand Metropolitan later merged with Guinness in '97 to create Diageo, PLC.
Among the usual places you can find a Burger King, there are a number of more esoteric locations like Sydney (Australia), Turkey, Paraguay, New Zealand (and old Zealand, too) and Madrid (Spain).