It was Arsenal who went one season without a loss.
Regular Season the Colts do
If you are referring to regular season games, then the Indianapolis Colts hold the record with 23 wins. (2008-2009)
Between 1970-1979, the Dallas Cowboys had the most regular season wins in the NFL with 105. The Miami Dolphins were second with 104 regular season wins.
As of as of March 8, 2012 The NFL team who has the most regular season wins since 1970 are the Pittsburgh Steelers with 396 regular wins since 1970.