Let's say that, in order to qualify for this ignominy, a team has to have had at least 2 Super Bowl appearances. My top 3 contenders for the award:
Denver Broncos. Yes, they've won 2 Super Bowls, but they've lost 5, including two of the worst beatdowns, both against NFC West teams--San Francisco, 55-10, the worst rout in Super Bowl history, in January 1990, and Seattle, 43-8, today. Those two games are two of the Super Bowl's 4 worst games in terms of point differential.
Buffalo Bills. They went to 4 consecutive Super Bowls in 1991-1994 and lost them all. The third of those, against Dallas, ties today's game with Denver for the worst point differential in a game.
Minnesota Vikings. Been 4 times, lost them all by at least 10 points.
Feel free to vote for one of these teams, or choose your own.