The Kansas City Chiefs and the Green Bay Packers
Uh... A lot of teams.
The Pittsburgh Steelers and the Arizona Cardinals
The Eagles went to the Super Bowl in 1980 and 2004.
Colts & Saints
The quarterback that was on the most Super Bowl teams was backup Gale Gilbert. He was on the roster of the four Buffalo Bills teams that went to the Super Bowl (Super Bowls XXV through XXVIII) and the San Diego Chargers team that played in Super Bowl XXIX, a total of five Super Bowls. Incredibly, his team lost the Super Bowl each time.
New York Jets vs Baltimor Colts
Through Super Bowl XLIV, one. That was the 2000 New York Giants that lost to the Baltimore Ravens in Super Bowl XXXV.