Dropped third strike
A dropped third strike can only occur when first base is not occupied or there are two outs. If the catcher does not catch the third strike, the batter is considered a baserunner and must be tagged or thrown out at first base for the out to be recorded. In the case the batter makes it safely to first base, the pitcher is credited with a strikeout (and the batter is also charged with one), but either a wild pitch or error is charged to justify the batter's presence on first base.
A dropped third strike is necessary for a pitcher to record four strikeouts in an inning, a feat which has been done many times.
The most famous instance of a dropped third strike occurred in Game 4 of the 1941 World Series, when Brooklyn Dodgers catcher Mickey Owen allowed a third strike to get past him, allowing Tommy Henrich of the New York Yankees to reach base and start a game-winning rally in the 9th inning. Another famous instance was in Game 2 of the 2005 ALCS, when A.J. Pierzynski of the Chicago White Sox reached base when Josh Paul of the Los Angeles Angels of Anaheim did not properly catch strike three with two outs in the bottom of the 9th; Pierzynski went on to score the game's winning run moments later.
The rule is a vestige of the earliest days of baseball, when a third strike was considered a ball in play, to be fielded like any batted ball. The rule remained in effect even though other rules regarding balls and strikes, catching balls, and the status of foul balls all changed over the ensuing decades and is now firmly entrenched.