The Boston Red Sox traded Babe Ruth to the New York Yankees in 1920. Prior to this, the Sox had won five of the first 15 World Series whereas the Yankees had never even played in one. The Yankees went on to 26 of them, while the Red Sox went 86 years without winning another.
In 1945, Billy Goat Tavern owner Billy Sianis brought his pet billy goat to a Chicago Cubs game. Several fans complained about the goat's odor and Sianis and his guest were asked to leave. Sianis is then said to have cursed the Cubs and promising that they'd never win the World Series again, and they haven't since 1908.
In 1919, the Chicago White Sox played the Cincinnati Reds in the World Series. The Sox lost, but it was later discovered that several of their star players took bribes to lose the games on purpose. These players were banned from baseball and it is said that their scandal cursed the team. The Sox did not win a World Series from 1917 to 2005.
King Tut was having an incredible season, hitting an astonishing .394 for the Washington Senators when his tomb and sarcophagus were violated but noted archaeologist Howard Carter. Tutankhamen slumped immediately afterward, barely finishing the year with a batting average of .200 and costing the Senators a playoff berth. He would never be the same afterward and within a couple of years was out of baseball, having supernaturally murdered all those who dared disturb his resting place.