The core of a game, which is an abstraction of the core or set of cooperative equilibrium states of an economy, is a fundamental notion of social equilibrium. However, except for games derived from special kinds of economic situations or satisfying restrictive (balancedness) conditions, the core is usually empty. In contrast, this paper shows that, with mild and economically natural assumptions, large games always have non-empty approximate cores. The game-theoretic framework is sufficiently general to cover a wide variety of economic situations.