I thought they were destroyed, but I was wrong. They go to needy kids in poor African countries. No kidding! Someday soon, some kid in Niger or Uganda will wear a T-shirt proclaiming the Chicago Bears the champions of Super Bowl XLI.
According to a marvelous New York Times article, the 288 sets of caps and T-shirts that the losers WOULD HAVE gotten, go to a warehouse and are ultimately destined for some developing country, where they likely don't know who won the Super Bowl ... or even know what the Super Bowl is. For them, a Super Bowl is one filled with food.
Major League Baseball, in fact, destroys the losers' gear. The NBA gives it to a charity. But as the NYTimes said, the NFL's loser-gear goes far, far away and "there, and only there, the losers get to be winners."