A gaming system and method for exchanging one or more triggered individual bonus games for one or more current plays of a community game or one or more future plays of a community game. If an individual bonus game is triggered in association with an individual gaming device, the gaming system enables the player to: (i) play the triggered individual bonus game, (ii) skip the individual bonus game and play or participate in a community or group game, or (iii) skip the individual bonus game and save an entry to play or participate in a future community or group game. In these embodiments, the gaming system determines one or more features or attributes of the available community game (which the player may play or defer play of) based, at least in part, on which of a plurality of different individual bonus games are triggered.