St. Louis Rams. Current cold streak is 17 games.
The current longest NFL losing streak as of October 12, 2011 are the Miami Dolphins with 7 consecutive losses going back to December 19, 2010
The Redskins are the longest but its Pittsburgh that is second! The Washington Redskins and the Denver Broncos have the two longest!
As of week 14 of the 2007 NFL season, the player who has played in the most consecutive games is current New York Giants punter Jeff Feagles. He is at 317 consecutive games and counting.
New England Patriots---The patriots lost their last game in the playoffs