Not the "World Series" as it is today - this series was between the American Association and Championship League Club, before these professional leagues fell and the modern World Series of American League vs. National League began in 1903. (I can't find much information on this series or the "Championship League Club", if anyone has more/more accurate information please let me know.)
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In 1894, Pittsburgh's owner William C. Temple offered a championship trophy to the winner of a best-of-seven-game series between the National League's first and second-place teams. In addition, he stated that the winning franchise would receive 65% of all ticket sales and the losing team would pocket 35%. Temple's novel idea would last for the next three years and helped to build the foundation for baseball's post-season popularity. More changes were on the horizon and in 1901, the American League was established much to the dismay of the senior circuit. Suddenly, baseball found itself engaged in a "civil war" as both rival leagues competed separately for the fan's loyalty and attention. Two years later a truce, previously known as the "National Agreement", was redefined outlining baseball's employment, salary and travel requirements. The 1903 compromise produced the business blueprint for major-league baseball and resulted in a merger that has lasted to this day. Once again Boston and Pittsburgh, the top American and National League teams, found themselves competing against one another in the first official "World Series". -Baseball Almanac
1903 World Series - Boston Americans (5) vs. Pittsburg* Pirates (3)
*In 1903, Pittsburgh was spelled Pittsburg without the ending h.
1905 World Series - New York Giants (4) vs. Philadelphia Athletics (1)
1911 World Series - New York Giants (2) vs. Philadelphia Athletics (4)
1913 World Series - New York Giants (1) vs. Philadelphia Athletics (4)
1914 World Series - Boston Braves (4) vs. Philadelphia Athletics (0)
1919 World Series - Cincinnati Reds (5) vs. Chicago White Sox (3)
1920 World Series - Brooklyn Dodgers [Robins] (2) vs. Cleveland Indians (5)
1927 World Series - New York Yankees (4) vs. Pittsburgh Pirates (0)
1931 World Series - Philadelphia Athletics (3) vs. St. Louis Cardinals (4)
1933 World Series - New York Giants (4) vs. Washington Nationals [Senators] (1)
1934 World Series - St. Louis Cardinals (4) vs. Detroit Tigers (3), Game 7
1942 World Series - St. Louis Cardinals (4) vs. New York Yankees (1), Game 5
1952 World Series - New York Yankees (4) vs. Brooklyn Dodgers (3)
1956 World Series - Brooklyn Dodgers (3) vs. New York Yankees (4), Game 5
1962 World Series - San Francisco Giants (3) vs. New York Yankees (4)
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World Series programs and scorecards from the Baseball Hall of Fame [link]
More programs and info at Sports Collectibles [link]
More info at FC Associates [link]
Even more info at Collectors Weekly [link]