We define and discuss Savage games, which are ordinal games of incomplete information set in L. J. Savage's framework of purely subjective uncertainty. Every Bayesian game is ordinally equivalent to a Savage game. However, Savage games are free of priors, probabilities, and payoffs. Players' information and subjective attitudes toward uncertainty are encoded in the state-dependent preferences over state contingent action profiles. In the class of games we consider, player preferences satisfy versions of Savage's sure-thing principle and small event continuity postulate. Savage games provide a tractable framework for studying attitudes toward uncertainty in a strategic setting. The work eschews any notion of objective randomization, convexity, monotonicity, or independence of beliefs. We provide a number of examples illustrating the usefulness of the framework, including novel results for a purely ordinal matching game that satisfies all of our assumptions and for games for which the preferences of the players admit representations from a wide class of decision-theoretic models.