According to psychology, affective empathy is one of the key processes governing human interactions. It refers to the automatic transmission and diffusion of emotions in response to others' emotions, which gives rise to emotional contagion. Contrary to other forms of empathy, affective empathy has received little attention in economics. In this paper, we augment the standard game-theoretic framework by allowing players to affectively empathize. Players' utility functions depend not only on the strategy prole being played, but also on the realized utilities of other players. Thus, players' realized utilities are interdependent, capturing emotional contagion. We offer a solution concept for these empathetic games and show that the set of equilibria is non-empty and, generically, finite. Motivated by psychological evidence, we analyze sympathetic and antipathetic games. In the former, players' utilities increase in others' realized utilities, capturing unconditional friendship; whereas in the latter the opposite holds, resembling hostility.