Back in 1919, the Boston Red Sox owner Harry Frazee sold Babe Ruth to the rival Yankees in a move that stunned fans and single-handedly changed both teams for years to come. For the Yankees, they got one of the best hitters ever, while the Red Sox received the "Curse of the Bambino" which didn't allow them to win another World Series for 86 years.
What could've been: Babe Ruth was an icon with the Yankees, so we have no reason to believe he wouldn't have put up the same gaudy numbers with the Red Sox. This wouldn't necessarily guarantee any titles, but we'd be hard pressed to believe they couldn't grab a couple as their rival Yankees would be without Ruth. "The Curse of the Bambino" would also not exist, therefore, making the Boston/New York rivalry obsolete.