There have been many dramatic on-and-off-field moments in over 130 years of Major League Baseball:
Gambling scandals
Baseball had frequent problems with gamblers influencing the game, until the 1920s when the Black Sox Scandal and the resultant merciless crackdown largely put an end to it. The scandal involved eight players and all were suspended for life.
1877 Louisville Grays scandal
After a losing streak towards the end of the season cost the Louisville Grays the pennant, members of the team were discovered to have thrown games for money. Four players, including star pitcher Jim Devlin, were banned from professional baseball for life.
1908 bribery attempt
On the eve of the "playoff" or "makeup" game between the Chicago Cubs and the New York Giants that would decide the National League championship, an umpire refused an attempted bribe intended to help the Giants win. The Giants lost to the Cubs, and the matter was kept fairly quiet. It came out the following spring, but the results of the official inquiry were kept secret. However, the Giants' team physician for 1908 was reportedly the culprit and was banned for life.
Recent research has suggested that the team physician was allowed to be the "scapegoat"; some baseball historians now suspect that the Giants' manager, John McGraw, was behind the physician's bribe attempt, or that it may in fact have been McGraw himself who approached the umpire. If true, and had it become known, it could have been disastrous, as McGraw was such a prominent figure in the game.
1914 World Series upset
The four-game sweep of the Philadelphia Athletics by the Boston Braves in the 1914 World Series was stunning. Students of that Series suspect that the Athletics were angry at their notoriously miserly owner, Connie Mack, and that the A's players did not give the Series their best effort. Although such an allegation was never proven, Mack apparently thought that it was at least a strong possibility, and he soon traded or sold all of the stars away from that 1914 team. The A's team was decimated, and within two years they limped to the worst single-season win-loss percentage in modern baseball history (36-117, .235); it would be over a decade before they recovered.
1917–1918 suspicions
The manner in which the New York Giants lost to the Chicago White Sox in the 1917 World Series raised some suspicions. A key play in the final game involved Heinie Zimmerman chasing Eddie Collins across an unguarded home plate. Immediately afterward, Zimmerman (who had also hit only .120 during the Series) denied throwing the game or the Series. Within two years, Zimmerman and his corrupt teammate Hal Chase would be suspended for life, not so much due to any one incident but to a series of questionable actions and associations. The fact that the question of throwing the Series was even raised suggests the level of public consciousness of gamblers' potential influence on the game.
Then, just a year ahead of the infamous Black Sox scandal, there were rumors of World Series fixing by members of the Chicago Cubs. The Cubs lost the 1918 Series in a sparsely-attended affair that also nearly resulted in a players' strike demanding more than the normal gate receipts. With World War I dominating the news (as well as having shortened the regular baseball season and having caused attendance to shrink) the unsubstantiated rumors were allowed to dissipate.
1919 conspiracy
The 1919 World Series resulted in the most famous scandal in baseball history, often referred to as the Black Sox Scandal. Eight players from the Chicago White Sox (nicknamed the Black Sox) were accused of throwing the series against the Cincinnati Reds.
Details of the scandal remain controversial, and the extent to which each player was said to be involved varied. It was, however, front-page news across the country when the story was uncovered late in the 1920 season, and despite being acquitted of criminal charges (throwing baseball games was technically not a crime), the eight players were banned from organized baseball (i.e. the leagues subject to the National Agreement) for life.
Although betting had been an ongoing problem in baseball since the 1870s, it reached a head in this scandal, resulting in radical changes in the game's organization. It resulted in the dissolution of the National Baseball Commission and the appointment of a Commissioner of Baseball (Kenesaw Mountain Landis) who took firm steps to try to rid the game of gambling influence permanently.