There are surprise teams in baseball every year. A club that was terrible the year before, suddenly gets a breakout player or an overperformer, who elevates them into the realm of annual contenders. Most of these examples, however, are nice stories that fizzle out in the playoffs.
On the other hand, a few of these squads keep the run going into the World Series, and those runs will never be forgotten. In 2011, the Cardinals faced "insurmountable" deficits repeatedly in the season's final month and a half, and they have overcome to this point.
Teams are listed chronologically, not in order of unlikelihood.