Since the NFL was restructured in 2002, there are four teams that have not played in the postseason as a wild card. The Patriots, Bears, Texans and Buccaneers have either won their division or missed the playoffs completely.
In the same time frame, the Patriots have made 14 postseason appearances. Combined, the Bears, Bucs and Texans have made 10 appearances.
Amount of wild card appearances is a good metric for the continued strength of a division as a whole. The graphic below displays each division and the number of wild card appearances since 2002. The AFC North comes out on top, boasting five consecutive seasons from 2008-2012 in which they sent at least two teams to the postseason. The AFC East and NFC West each finished with only six appearances.