Adam Dunn currently has a 32 game streak which seem high to me.
Anthony Young: 27 Games, May 6, 1992 to July 24, 1993
David Cone is the only Mets pitcher to pitch 3 consecutive complete game victories. Mike Pelfrey threw 2 in 2008
Joe Dimaggio holds the record for consecutive games with a hit with 56 games!
Joe DiMaggio set the record with hits in 56 consecutive games in 1941.
Cal Ripken Jr. played in 2,632 consecutive games.
The MLB consecutive games with a base hit record is held by Joe DiMaggio of the New York Yankees who got a hit in 56 consecutive games in the 1941 season.
Mikey Manning with 26 games
In 1904, Jack Taylor of the Cubs set a major league record by pitching 39 consecutive complete games. Taylor actually threw 187 consecutive complete games between June 1901 and August 1906, but this streak was interrupted by 15 additional relief appearances. Thus Taylor appeared in 202 consecutive games without being relieved himself. Of course, this was in the 'dead ball' era.