Answer:
As of the 2010 Super Bowl, 14 of the 32 NFL teams have never won a Super Bowl (4 have never been in one):
Minnesota Vikings (0-4)
Buffalo Bills (0-4)
Cincinnati Bengals (0-2)
Philadelphia Eagles (0-2)
Tennessee Titans (0-1)
San Diego Chargers (0-1)
Atlanta Falcons (0-1)
Carolina Panthers (0-1)
Arizona Cardinals (0-1)
Seattle Seahawks (0-1)
Cleveland Browns
Houston Texans
Jacksonville Jaguars
Detroit Lions
Technically the Chiefs and the Jets only won Super Bowls as AFL teams and never as NFL teams.
Prior to the 1970 merger of the AFL with the NFL the Eagles won 3 NFL championships('48, '49, '60), and the Vikings won one in '69. The Lions have won 4 NFL Championships: '35, '52, '53 and '57. Arizona Cardinals won one (in Chicago) in '47 and the Cleveland Browns won 4, the last one in 1964. The first Superbowl was held in January, 1967. Championships prior to that were not Super Bowls.