I don't think there's a rule about this, but maybe it's a matter of etiquette. Nearly every player I've encountered puts the pieces they capture next to the board, but I've met some who like to store the pieces as soon as they capture them (maybe they are "neat freaks"? :-).
I found this a bit unsettling, but maybe it's just me? I must admit that I semi-consciously use the captured pieces for counting in the early parts of the game, when most of the pieces are still on the board. I also suppose that it could be inconvenient to have to ask the other player to dig out your dead queen in case of a promotion (that situation didn't arise in my experience, however).