The Celtics/Lakers might be the biggest rivalry in basketball, but the Yankee/Red Sox rivalry is the greatest in the MLB world. In the 2004 American League Championship Series, the chance of the Yankees winning the series looked good, as the team led the series 3-0. Game 4, however, changed the tide, and the Red Sox went on to make history with a four-game winning streak to clinch the ACLS and move onto the World Series, which they won against the St. Louis Cardinals — their first time in 86 years.