The National Football League began in 1920 as the American Professional Football Association.
The "All America Football Conference" competed from 1946 through 1949. After the 1949 season, three of its teams were admitted into the NFL:
Cleveland Browns
Baltimore Colts (drop out after 1950, a new Baltimore Colts team started in 1953)
San Francisco 49ers
The "American Football League" competed from 1960 through 1969. All ten teams entered the NFL in 1970 as part of a 1966 merger agreement. There were four different American Football Leagues over the years; this one, the fourth and the only one to last more than two years, changed the nature of professional football in America.
The "World Football League" competed in 1974 and part of 1975.
The "United States Football League" competed from 1983 through 1985.
The "Arena Football League", which plays an indoor version of American Football, has been competing since 1987.
The "World League of American Football" competed independently for a couple of years in the 1990s, before being transformed into NFL Europe, whose teams act as farm clubs for those in the NFL proper.