Below are the number of reported player arrests per NFL team since 2006. Rather than present the results in a straight 1-32 list, I decided to break them down by division, just to give you a better idea of how teams compare to their biggest rivals. These figures do not take conviction into account. Being taken into police custody is the only qualifier cited. For the sake of divisional "standings", ties were broken by dropping the least recent year.
Overall, the Saints rank 15th (i.e., middle of the pack), with 1st being the least often arrested. That includes a "since 2007" tiebreaker with Oakland, which they win, by virtue of Jammal Brown's 2006 domestic abuse arrest falling off their collective rap sheet.
The "best behaved" team, at least according to these figures, is the Arizona Cardinals, with only four arrests over the last seven years. Of note is the relatively low arrest totals of both the Giants and Jets. In a metropolitan area the size of NYC, it's rather impressive to see those guys keeping their noses clean. The Cincinnati Bengals regrettably lead the league in arrests since 2006, though that shouldn't come as a surprise to anyone.
The database goes back to 2000, btw. I simply limited the presentation range, in order to make the figures more relevant to the Sean Payton era. It's also sortable by position and appears to be updated regularly, as it includes the Aaron Hernandez and Ausar Walcott arrests of the past few days. Nice bookmark material.
Dallas Cowboys 8
Philadelphia Eagles 9 (7 since 2007)
New York Giants 9 (9 since 2007)
Washington Redskins 12
Arizona Cardinals 4
St. Louis Rams 8 (7 since 2007, 4 since 2008)
San Francisco 49ers 8 (7 since 2007, 7 since 2008)
Seattle Seahawks 16