Souvenir
In ballparks across the world fans hold their collective breath waiting to see if players will make the catch. In a nifty parallel, many crowds will also cheer when fans catch foul balls and home runs. There are exceptions of course -- you better be sure it's foul or "outta there" before you go for it. If you don't it gives birth to infamous moments in which a Cub fan is hated forever or Sheffield decks a guy in the stands for getting in his space. With that in mind, if you're in the right and you catch it -- the ball is yours. A moment of glory and a souvenir that the management will let you take home. Nice. Unless you find yourself in Fenway -- where, in addition to your moment and your ball, you better be ready to be handed a critique of your catch.
What gets the biggest hand? A kid catching a ball.
What gets booed? If you drop it after catching it of course or spill your drink/hot dog/popcorn while trying. Also, if your drunken ass falls on the field while reaching for it.
Then there is a middle ground I had no idea of until I heard a discussion of the subtleties of the craft. An adult will not be given a hardy cheer if he catches the ball in a glove. At a game once, I heard fans give the raspberry to this. Apparently, for adult males -- it is bare-handed or nothing.
Having revealed the rougher side of the critique -- I must, in all fairness say that Red Sox fans will also defend their own in these moments. The night John Lester pitched his no-hitter, I was sitting way down the third base line and saw a man hit in the face by a singing line-drive foul. Another fan caught it in rebound and held it up for the cheer. He was booed. The fan-catch-code clearly rules that if a fan gets hit in a face the souvenir belongs to him/her. The rebounder would not give it up -- and everyone in my section agreed -- that was some cold shit.