Johnny Bench won his ten Gold Glove awards consecutively, from 1968-1977.
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Derek Jeter won his five Gold Glove Awards in 2004, 2005, 2006, 2009 and 2010.
Ivan Rodriguez won 13 Gold Glove Awards as a catcher. 1992 - 2001, 2004, 2006, and 2007.
Mickey Mantle won his only Gold Glove award in 1962.
Greg Maddux with 18
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Cincinnati Reds
As of the start of the 2008 season, Andruw Jones has won 10 Gold Glove awards. He has won the award every year between 1998-2007.
Pitcher Jim Kaat won 16 consecutive Gold Glove awards ... 14 in the American league between 1962-1975 and two in the National League between 1976-1977.
Through the 2010 season, 13. He won the Gold Glove for 10 straight seasons between 1992-2001, 2004, 2006, and 2007.