The Major League Baseball team with the most consecutive scoreless innings is 56 by the Pittsburgh Pirates. They have held that record since 1903.
I think35 innengs
Well this isn't the all time answer, but i know for a fact the Yankees just held the Red Sox to a Red Sox team record 31 scoreless in their sweeping of the Red Sox tonight
In 1966, the Baltimore Orioles did not give up one single run -- earned or unearned -- to the L.A. Dodgers in the last 33 innings of the Series.
Babe Ruth with 29 2/3 consecutive scoreless innings pitched in World Series play.
In 1903 the Pittsburg Pirates were held scoreless for 52 innings.
In 1910 The Portland Beavers won their second Pacific Coast League title, achieving a remarkable record in the process; the Beavers pitchers threw a baseball record 88 consecutive shutout innings.
Any team that had an opposing pitcher throw a perfect game or no hitter