The fewest sacks allowed by a team in an NFL season is 7 by the 1988 Miami Dolphins. Dan Marino was sacked 6 times in 606 pass attempts that season.
In a non-strike season, 16 game season the NFL record for fewest sacks in a season is 13 by the 1981 Baltimore Colts. The 2008-2009 Kansas City Chiefs in 16 games I think only had 9 sacks 1988 Miami Dolphins only allowed 7.
The NCAA team record for sacks is held by Texas Christian University who sacked the University of Nevada QBs 15 times in a game played September 9, 2000.
The most losses by a team in NBA history was by the 1972-73 Philadelphia 76ers who had a regular season record of 9-73.
The 1984 Chicago Bears who had 72 sacks.
The 1986 Chicago Bears
In the NFL, as of the 2008 season the record for most sacks in a season by a team is 72 by the 1984 Chicago Bears.
The Chicago Bears hold the NFL team record with 72 sacks in 1984.
Texas A&M 1991 - 56 sacks
In the 2007 NFL season, there were 1102 total sacks so the average team was sacked 2.2 times per game (34.4 times per season). In 2006, there were 1164 sacks averaging out to 2.3 sacks per game per team (36.4 sacks per season) and in 2005, there were 1182 sacks averaging out to 2.3 sacks per team per game (36.9 sacks per season).
Purdue with 33 sacks
The season hasn't ended yet but so far it is the bears with 31 sacks. If you meant 2009 then it was the green bay packers at 51 sacks.
the chargers do
The Dallas Cowboys led the league in sacks with 59.