Score: This is a symbolic affirmation of the player’s skill, and encourages her to be competitive in her play in order to best the scores set by herself, and dependant on the context, others. In older, simpler games, this is all the reward anyone would get, besides a meager bit of story to provide closure at the end of a game.
Abilities: New abilities allow the player to exert a higher degree of control over the game world than previously available; however, new challenges should render these abilities to be necessities rather than just conveniences. Granting more abilities allows the player to feel as though she is slowly taking over the game world, and as though she is nearing a God-like status within it. This rise to power is immensely satisfying, and the pacing of it is central to making a game enjoyable (games in the Metroid series generally nail this). Gaining new playable characters can in a sense imbue the player with new abilities, unless they add another type of gameplay to the title altogether (à la Sonic Adventure’s non-Sonic characters), in which case another game mode would be effectively created.
Areas/Terrain: The value is obvious: new places give the player more to explore, and more tasks to accomplish. This is a valuable and important reward to give the player in any type of game.
Story: This only used to serve as a significant reward in games primarily concerned with stories, such as RPG’s. However, more and more games (particularly American-developed) have begun to use story as reward in a wider variety of genres. One unfortunate, yet common use of story is as a distracter from weak gameplay; a compelling narrative can often redirect attention away from long, boring stretches of repetitious fighting (say, in a turn-based RPG with a very limited battle system.)
Game Modes: This either signifies a different difficulty setting, or a part of the game that is in its own right, a game of its own (though more than a mini-game.) Examples of the second type include versus modes in genres such as racing and fighting.
Kitsch: Items, either within the context of the game’s world or not, that hold special sentimental/totemic value but do not directly affect the gameplay (includes things like sound tests, art galleries, etc.) Useful items that are especially desirable because of their aesthetic properties (say, a costume that while increasing defense, looks really pretty) can be said to have “kitsch value”.
Next up? A look at the behaviors (from a gaming perspective) exhibited by the player that the game will reward.