Public goods games study the incentives of individuals to contribute to a public good and their behaviors in equilibria. In this paper, we examine a specific type of public goods game where players are networked and each has binary actions, and focus on the algorithmic aspects of such games. First, we show that checking the existence of a pure-strategy Nash equilibrium is NP-complete. We then identify tractable instances based on restrictions of either utility functions or of the underlying graphical structure. In certain cases, we also show that we can efficiently compute a socially optimal Nash equilibrium. Finally, we propose a heuristic approach for computing approximate equilibria in general binary networked public goods games, and experimentally demonstrate its effectiveness. Due to space limitation, some proofs are deferred to the extended version.