In the first round of the 2009 MLB Playoffs featuring the Minnesota Twins and the New York Yankees, Twins catcher Joe Mauer hit a fly ball down the left field line that fell in front of Yankees outfielder Johnny Damon clearly in fair territory but it was called foul. The Twins lost the game and the series, which featured many poor umpiring calls. For this reason and many others, there should be Instant replay for non-homerun calls in the postseason.
The first reason there should be instant replay in the postseason is plain and simple: To get the right call. The wrong call on any play (or plays) can cost a team the game and the series and can also cause disrespect to the umpires. Example: Don Denkinger was the umpire at first base in game 6 of the 1985 World Series. With the Cardinals leading the Royals three games to two, the Cardinals had taken a 1-0 lead into the eight inning. Todd Worrell came in for the Cardinals in the ninth to face Jorge Orta, who hit a slow roller to first baseman Jack Clark. He tossed it to Worrell covering first base. Denkinger called Orta safe, thought television replay showed he was out by half a step. The Royals went on to win Game 6 and the World Series.
Secondly I would like to say why only to have instant replay in the postseason and not include the regular season as well. I think it should only be used in the games that count, not in a September game between two last-place teams. MLB might like to use instant replay in the reg. season for individual stats or accomplishments, such as the infamous call by Jim Joyce in the non-perfect game by Armando Galarraga.
The third reason is this: to prove the real champion. If the winner of the ALCS, NLCS, World Series, etc. won it or got there because of a bad call, it would be to some degree tainted
That is why there should be instant replay in the postseason. To get the right calls and crown the true champion.