Which NFL teams have faced each other the fewest times...and the most?

These numbers are subject to change but, as of this posting (near the end of the regular season 2015-2016)

The league's newest franchise is the Houston Texans. Owing to a very rigid schedule rotation all teams play each other on a regular rotating pattern which began in 2002 the first year the Texans played. Consequently they have seen many opposing teams an equal number of times. The current least seen matchup is Houston vs. 8 different teams (the entirety of the NFC North and NFC West divisions), having occured only 3 times.

The teams who have seen each other the most are the Green Bay Packers and Chicago Bears (formerly Chicago Staleys and Decatur Staleys) who have faced off 192 times (190 regular season and 2 playoff games)

http://www.pro-football-reference.com/teams/htx/head-to-head.htm
http://www.pro-football-reference.com/teams/gnb/head-to-head.htm