Event cameras capture the world at high time resolution and with minimal bandwidth requirements.However, event streams, which only encode changes in brightness, do not contain sufficient scene information to support a wide variety of downstream tasks.In this work, we design generalized event cameras that inherently preserve scene intensity in a bandwidth-efficient manner.We generalize event cameras in terms of when an event is generated and what information is transmitted.To implement our designs, we turn to single-photon sensors that provide digital access to individual photon detections; this modality gives us the flexibility to realize a rich space of generalized event cameras.Our single-photon event cameras are capable of high-speed, high-fidelity imaging at low readout rates.Consequently, these event cameras can support plug-and-play downstream inference, without capturing new event datasets or designing specialized event-vision models.As a practical implication, our designs, which involve lightweight and near-sensor-compatible computations, provide a way to use single-photon sensors without exorbitant bandwidth costs.