The New England Patriots have won:
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They hold the record of 21 consecutive games won, spanning the period of October 2003 to Halloween 2004 - 18 regular season games and three playoff games.
WINNING SEASONS -
1961-4, 1966, 1976-80, 1982, 1984-8, 1994, 1996-8, 2001-9 - for a total of 29 winning seasons.