The hallmark of a NonZeroSumGame is synergy: players working together can realize higher group and invididual point totals than they could invidually, whereas this is impossible in a ZeroSumGame.
PrisonersDilemma and IteratedPrisonersDilemma are simplified examples of non-zero-sum games.
Economy is a NonZeroSumGame. Although the amount of money is (kind of) fixed the value that can be generated and owned is infinte. Other examples are FreeSoftware, Wiki, NewsNet?, ...
Farming is a NonZeroSumGame. If one farmer figures out how to water his tomatoes to increase his crop, it doesn't reduce the amount of tomatoes other farmers can grow. If 2 farmers independently figure out 2 different ways to increase their crops, each of them can maximize the amount of tomatoes each of them individually grows by sharing their ideas and applying both ideas to their tomatoes.
Baseball, Football (both kinds) and in fact most competitive sports are NonZeroSumGames, whereas most board games (chess, checkers, monopoly), are ZeroSumGames.
A good way to begin to analyze non-zero-sum games by converting them to easier-to-analyze ZeroSumGames. But that neglects the difference between a game where I end up with 2 houses while someone else ends up with 5 houses, vs. a game where I end up homeless and someone else ends up with one house. Neglecting that difference leads to cynicism and schadenfreude. -- DavidCary