New York Yankees (1921–1964)
20 World Series titles and 29 AL pennants in 44 years. Never has another professional sports team been so dominant. The Yankees won almost half of all the World Series titles during this 4 decade dominance. Legendary players such as Babe Ruth, Lou Gehrig, Joe DiMaggio, Yogi Berra, Mickey Mantle etc played for the team during this dominant time.
Boston Celtics (1957–1969)
13 seasons. 11 Championships (8 won in a row). 12 Finals. This coincides also with Bill Russell’s career, which started and ended at the exact same times. No other NBA team has been so dominant. Only lost one Finals during this remarkable span. No other player in professional sports history has as many rings as Bill Russell. In addition to Russell, this legendary dynasty contained such HOFers as Bob Cousy, Tom Heinsohn, Bill Sharman, Sam Jones, and John Havlicek.
Montreal Canadiens (1953–1979)
During this 27 year period, the Canadiens won a remarkable 16 Stanley Cups, almost 60% of the time! Such legendary NHL players as Maurice “Rocket” Richard, Jean Beliveau, Henri Richard, Ken Dryden, Guy Lafleur played for the Canadiens during this time.
Green Bay Packers (1961–1967)
5 Super Bowl wins in 7 years. Not quite as long a period of dominance as the other teams I mentioned but as dominant an NFL team as you can get. They had such notable HOFers as Bart Starr, Jim Taylor and Paul Hornung.