Since the first official World Series in 1903, there have been about 1,200 major league post-season games, split virtually evenly between about 600 World Series games and 600 league playoff (league championship series or division series) games.
Of those 1,200 games, only 4 have ended on an error. The New York Mets were the winners in two of those four games -- in both cases giving the Mets their third win of a World Series. These were the only two World Series championships in Mets history. These two walk-off errors are, naturally, two of the most famous plays in Mets history, and among the most famous in all World Series history: the Buckner error on Mookie Wilson's grounder to first in 1986, of course, and J.C. Martin's sacrifice bunt attempt (with men on first and second, nobody out) in the 10th inning of the 4th game of the 1969 World Series -- the throw to first by Orioles pitcher Pete Richert hit Martin in the elbow and caromed away, allowing pinch runner Rod Gaspar (Jerry Grote had doubled to lead off the inning, and Al Weis was on first after an intentional walk) to score from second base for the winning run.
The other two walk-off errors in post-season history were:
--The third game of the 1914 World Series. Connie Mack's perennially powerful (three World Series championships in the previous four years) Philadelphia A's already trailed the underdog Boston Braves 2 games to none. The A's thought for sure they had their first win of the Series notched when they scored two runs in the top of the 10th, but the Braves came back and scored two of their own in the bottom of the tenth. And in the bottom of the twelfth, a sequence unfolded similar to the Mets' last inning in the J.C. Martin game. Hank Gowdy doubled for the Braves, just as Jerry Grote doubled for the Mets in that fateful 1969 game. And just like Grote, Gowdy was replaced by a pinch-runner. And just as Al Weis was then intentionally walked in 1969, so in 1914 was the Braves' Larry Gilbert. And just like J.C. Martin in '69, Herbie Moran in 1914 laid down a bunt that was fielded by the pitcher, in this case the A's Joe Bush. But unlike Pete Richert in 1969, Bush opted to try to get the lead runner at third -- and threw the ball away, allowing the runner to score from second to end the game. The Braves went on to sweep the Series, and Connie Mack promptly dismantled his great team -- the A's dropped into last place for years thereafter.
-- After many years without a first place finish, the Yankees finally won the AL East in Joe Torre's first season as manager of the Yanks in 1996. The Yanks lost the first game of the best-of-five league division series to Texas at Yankee Stadium, and fell behind 4-1 in game 2 (the big blow a three run homer by Juan Gonzalez, who homered off of Johan Santana yesterday in Santana's spring training debut with the Mets). But the Yankees crept back with single runs in the 4th, 7th and 8th innings, while Mariano Rivera pitched two and two thirds perfect innings in relief of Andy Pettite and then John Wettlend pitched two more run-free innings -- the game was tied into the bottom of the 12th inning. Just as in the 1914 and 1969 World Series games, a first and second, no-out situation (Derek Jeter single, Tim Raines walk) led to an obvious sac bunt opportunity. Chunky Yankee third baseman Charlie Hayes, who had entered the game earlier as a pinch hitter for Wade Boggs (!) laid a bunt down toward third base where Dean Palmer (according to Win Shares, the worst fielder in major league history to play a significant number of innings at third base) picked it up but bounced his throw two feet in front of first and past second baseman Mark McLemore who was covering first on the bunt. Jeter came in to score and the Yankees won the rest of the games against Texas, the ALCS against Baltimore and the World Series against Atlanta, the first of four Yankee championships in a five year period. That 1996 Yankee team included not just Raines (36 years old) and Boggs (38 years old) in the stars-in-their-twilight category, but Darryl Strawberry (34 years old) as well. Charlie Hayes, who laid down the bunt that won this game for the Yanks, was the fielder at fault in the case of another historic error -- on August, 15 1990 Terry Mulholland pitched a game that would have consitituted a perfect game if not for an error by Hayes in the 7th inning (Wikipedia points out that more men have orbited the moon than pitched a perfect game).