As of August 9th 2009 2054 hundred hours it is the Boston REDSOX at 26 innings and still counting.
On June 27 2012, the LA Dodgers extended their scoreless streak to 30 innings by losing to the SF Giants by a shutout for the third straight game. The Dodgers next chance to extend their streak comes June 28 2012 vs. the NY Mets.
On April 15, 1968, the Mets and the Astros played an astonishing 24 innings of scoreless Baseball, until Houston's Norm Miller scored on an error in the bottom of the 24th.
Box: http://www.baseball-reference.com/boxes/HOU/HOU196804150.shtml
Gaylord Perry, 16 innings September 1, 1967. It was a 1-0 Giant win over Cincinatti at Cincy. The reliever who pitched last 5 innings got the win. Think it was Ron Herbel.
Babe Ruth in a 14 inning World Series complete game in 1916 gave up 1 run in the 1st inning followed by 13 scoreless innings which he won by a score of 2 to 1 .
Brandon Webb in 2007 with 42 1/3 consecutive scoreless innings.
The Red Sox record is 45 shutout innings by Cy Young of the 1904 team. During this streak he pitched 25 1/3 hitless innings, still a major league record. The American League record for shutout innings is 56 by Walter Johnson of the 1913 Washington Senators.
Brad Ziegler Oakland Athletics 2008 32 innings still going
Babe Ruth with 29 2/3 consecutive scoreless innings pitched in World Series play.
Cy young
Through the 2008 season, that is 55 2/3 innings by Walter Johnson of the Washington Senators between April 10, 1913 and May 14, 1913.
The record is 59 by Orel Hershiser of the Los Angeles Dodgers between August 30, 1988 and September 28, 1988. Don Drysdale did it back in either the 50's or the 60's, but he had a record 58.2 scoreless innings, which basically means 6 straight shutouts plus 2.2 extra innings. Orel Herseiser broke that record back in 1988 with 59.0 consecutive scoreless innings
The New York Yankees Mariano Rivera holds the all time Post season record of 33 1/3 scoreless innings pitched. Whitey Ford holds the World Series record with 33 consecutive scoreless innings pitched. Christy Mathewson pitched 27 consecutive scoreless innings in a single post season as he threw 3 shutouts in the 1905 World Series.
549873938737 innings
The MLB record was set by Oakland A's pitcher Brad Ziegler with 27 scoreless innings on Sunday July 27, 2008. The record of 25 scoreless innings was previously held George McQuillan of the 1907 Philadelphia Phillies.
The star lefty handed pitcher for the Boston Red Sox, Babe Ruth, established the record of 29 and 2 thirds consecutive scoreless World Series innings pitched. It was not till 1961 that Whitey Ford broke Babe Ruth's World Series record, at 33 innings.
In actual fact, the record is six centuries in consecutive Test innings, scored by Don Bradman between January 1937 and July 1938.