Ever since World War II, American teams have played in European Leagues (usually in US Army Leagues stationed around the World), or have played matches against teams from around the World (usually Under 19/20 representative teams from the USA).
Additionally the National Football League has played a number of games outside of USA, notably the matches against Canadian Football League opposition from 1950-1969, and the American Bowl / International Series of matches between NFL teams played in cities around the World.
A third feature of American Football on the World stage is the Professional Leagues played in Europe & North America which have attempted to be a World League.
Finally there is the American Football World Cup, first held in Italy in 1999, and other World Competitions such as American Football at the World Games or International matches between countries from around the World.
United States Air Force & Army Leagues:
National Football League International:
American Football World Cup: