Experienced something of a resurgence in the 1940s, but could never win a world championship. Were pretty dire/unpopular throughout the 1950s and 1960s, but then came out of nowhere in 1967 to reach the World Series, losing in 7 games to the St. Louis Cardinals. Suddenly became wildly popular in Boston and throughout New England. Still couldn't win a world championship, but came close in 1975, and then agonizingly, skull-crushingly close in 1986.
Failure to win world championship in 1986 spawned the creation of a moronic fiction known as "The Curse of the Bambino", which attributed the Red Sox' decades-old habit of stumbling at the final hurdle to a hex put on them from the Afterlife by Babe Ruth, presumably because he was angry that the team sold him way back when. (In reality, their inability to win the big one could be ascribed to a combination of piss-poor management and being on the wrong end of random chance at the worst possible times.)
Anyway, the media seized on "The Curse", beating Red Sox fans to death with it throughout the late '80s and beyond. National TV broadcasts of Red Sox games were filled with forced, gratuitous references to "The Curse" (announcers talking about it incessantly, showing still photos of Babe Ruth, etc., etc.). Yankee fans (at least the ones who were able to get out on parole) would hold up signs making reference to "The Curse" and delightedly chant "Nine-teen-eight-teen" (a mocking reminder of the year of the Red Sox' last World Series victory) at every possible opportunity during Red Sox-Yankees games at Yankee Stadium. All of this "Curse" business reached an absolute peak in 2003, when the Red Sox lost to the Yankees in an extraordinarily painful fashion in the American League Championship Series (1 step away from the World Series). And then...
In 2004, the Sox and Yanks met once more in the ALCS. The Yankees raced out to a three-games-to-none lead, needing only to win one more game before the Red Sox won four games in order to advance to the World Series. Here, let it be known that previously, NO TEAM IN THE HISTORY OF MAJOR LEAGUE BASEBALL HAD EVER COME BACK FROM A THREE-GAMES-TO-NONE DEFICIT TO WIN A PLAYOFF SERIES.
I could go into great detail on what happened next, but sufficed to say, the Red Sox stormed back to seize glorious victory from the Yankees, winning four games in a row. With their chief tormentors vanquished, they went on to comfortably defeat the St. Louis Cardinals in the World Series.
Having suffered through 86 years without a championship, including two decades of taking an infinite stream of s'hit from the media and from chucklehead Yankee fans with all of their "1918" bulls'hit, Red Sox fans predictably went buckwild, celebrating their asses off over because 1) their team had won its first world championship since World War I, and had done so in an absolutely remarkable manner; 2) they would stop taking endless s'hit from the media and from the mustachioed cretins and knuckle-draggers known as Yankee fans.
Of course, in spite of the fact that their joyous celebration was, in large part, a direct reaction to the crap that they had endured from the media and from Yankee fans for decades, there was a huge media backlash against this celebration, with loads of sports journos lining up to write articles bashing Red Sox fans for celebrating so vigorously.
And of course, Yankee fans needed something to fill the giant void in their lives, since their silly little "1918" chant was rendered useless over the course of two glorious weeks. But instead of having the balls to man up and eat crow, they reverted to their "26 championships to 6 argument", conveniently forgetting that it was the whole "1918" thing, much more so than the "26 championships" thing, that they had been rubbing in our faces forever.
Tough luck guys. And sorry about that little championship drought you've been having. Must suck to have won your last title way back in 2000.