Some "older", small market teams that have never made it to the Super Bowl: the Saints, Cardinals, and Browns. It's been 22 years since the Bengals, another small market team, made a Super Bowl appearance...and lost; and it's been 10 years since the Bills went to the Super Bowl...and lost.
As far as expansion teams go, the Panthers, the Ravens (the old Cleveland Browns) and the Titans (the old Houston Oilers) have been to the Super Bowl once each...losing two of three. The Texans and Jaguars have never been. Tampa Bay had been in the NFL 27 years before making their first Super Bowl appearance and winning. The other "old" expansion team in 1976 - the Seattle Seahawks, has never been to the Super Bowl.
Since the NFL salary cap began in 1993, three of the older, winning franchises - Denver, Dallas, St. Louis (the old Los Angels Rams) and Green Bay - have been to the Super Bowl two times, winning six of the eight Super Bowls between them (Green Bay lost to Denver). New England has been to the Super Bowl three times and won twice. Atlanta, another of the older franchises, has been once...and lost.
Bottom line: 8 of the 11 Super Bowls has been won by the older, "winning" teams since the cap was put in place.
Here's a decent link discussing the NFL cap system as a possible solution for the NHL...