Personally, I don't put as much credence on the supposed championships before the merger of the AFL and NFL, therefore, I prefer looking at the statistics since the merger, and when the Super Bowl began. Since that time ony the pies have made more playoff appearances than the Vikings. The Vikings have 10 more appearances than the Pukers.
The team that has made the most playoff appearances (1933 when playoffs started through 2009) is the New York Giants & Dallas Cowboys with 30, followed by St. Louis & Minnesota with 26, Green Bay & Pittsburgh with 25, Chicago & Cleveland with 24, Indianapolis with 23, Washington, Philadelphia, San Francisco, & Miami with 22, Oakland with 21, Tennessee with 18, Denver with 17, New England with 16, Detroit, Buffalo & Kansas City with 14, New York Jets with 13, San Diego with 12, and Seattle & Tampa Bay with 10, Atlanta and Cincinnati with 9, Arizona with 8, New Orleans with 7, Jacksonville & Baltimore with 6, and Carolina with 4. The Houston Texans are the only team currently in the NFL that have NEVER made a playoff appearance.
The team that has made the most playoff appearances since the AFL-NFL merger in 1966 (through 2009 playoffs) is Dallas with 30, Minnesota 26, Pittsburgh 24, Miami 22, Oakland, San Francisco & St. Louis Rams 21, Indianapolis Colts 19, Philadelphia & Tennessee 18, Denver 17, Green Bay, New England & Washington 16, Buffalo, Cleveland, Kansas City & New York Giants 14, Chicago & New York Jets 13, San Diego 12, Seattle & Tampa Bay 10, Atlanta, Cincinnati & Detroit 9, New Orleans 7, Arizona, Baltimore & Jacksonville 6, Carolina 4, Houston Texans are the only team currently in the NFL that have NEVER made a playoff appearance.