There are several. For the past ten-plus years the strongest rival has been the Indianapolis Colts; both teams have made the playoffs a combined 23 times since 1994 and have knocked one or the other out more often than any other two teams over the same period. Also take into account that the Colts were in the same division as the Patriots until the league created the fourth divisions in 2002 with the introduction of the Houston Texans.
Another bitter rival of the Patriots is the Denver Broncos, who own a winning record against the Patriots since 1983 and have defeated the Patriots twice in playoff matchups.
The New York Jets have been the Patriots' most bitter divisional rival; the two teams have split 100 career matchups and hold one tie (in 1966), while the Patriots own a 2-0 playoff edge. Jets successes or lack thereof have also cost the Patriots playoff berths for 2002 and 2008 as well.
The San Diego Chargers emerged as a bitter rival at the start of the 21st century with wins in 2002, 2005, and 2008 and Patriot playoff wins in 2006 and 2007.
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There are several. The Indianapolis Colts are their most famous conference rival. The New York Jets and Miami Dolphins are presently their key divisional rivals. The Patriots also share tense rivalries with the San Diego Chargers, Pittsburgh Steelers, and Baltimore Ravens.
The primary rivals of the New England Patriots are:
The rivalry with the Colts is the bitterest, with three playoff meetings in the last seven seasons and bitter losses to the Colts in 2006 and 2009.
The Patriots also share bitter rivalries with the Pittsburgh Steelers, the Denver Broncos, and the San Diego Chargers.
The Patriots more recognized rivals would be their AFC east rivals such as NY Jets, Miami Dolphins, and Buffalo Bills. However Patriots do share outside rivalries and possibly stronger rivalries with The Denver Broncos and Indianapolis Colts.
Their main rivals are in their division - the NY Jets, the Miami Dolphins, and the Buffalo Bills.
Other rivals include the Indianapolis Colts (due to the quarterback rivalry between Tom Brady and Peyton Manning), and the NY Giants (who beat them on a last-minute play in the 2008 Super Bowl and again in the 2012 Super Bowl).
With the 2011 ascension of Tim Tebow followed by his release and Peyton Manning's trade to the Denver Broncos, a long-time rivalry was intensified. The ascension of Andrew Luck as Colts quarterback has kept the Colts a playoff contender, though 2013 will mark the first time since 2002 the Patriots do not play the Colts in the regular season.
The Baltimore Ravens' recent playoff successes have created a true rivalry there as well.
The Patriots rivals are:
The New York Jets
the Miami Dolphins
the Baltimore Ravens
the Denver Broncos
Former rivalries that have kind of fallen off of late
the Indianapolis Colts
the San Diego Chargers