Babe Ruth set the season home run (HR) record in 1919, 1920, 1921, 1927. In both 1920 and 1927 Ruth hit more HR than any other team in his league. In 1927 Ruth set the standard with 60 HR.
I created a file with team HR data from 1919 through 2011: max, min, ave, StDev. Click this link to view the data and graphs. Seasons in which the max or min was less than 60 are in red.
Excluding the short 1981 season:
From 1927 through 2012 teams have failed to hit at least 60 HR 116 times, most recently the St. Louis Cardinals with 58 in 1986.
1927-2012: 204 times teams have hit fewer than the current record of 73 HR set by Barry Bonds in 2001. Most recently: LA Dodgers 72 in 1992.
1977-2012: average HR per team over 100 each season.
1996-2012: minimum HR below 100 in three times - 2008, 2009, 2011 all in the National Conference (NC).