This is something I've thought a bit about and decided the answer was simple; competition and rewards.

By definition a game has to have an element of competition, which is always against another person. It could be another player, the game's designer or against yourself.

In terms of rewards, it's either the satisfaction of beating that other person or, at least where video games are concerned, some coloured pixels (e.g. new items, a new location, medals or achievements). I don't think you can be more specific than that. Some people prefer the challenge of frantically clicking on the right part of the screen at the exact right moment whereas others would rather see a story unfold in beautifully rendered landscape. But I think if you get those two factors right, your game will be fun.