Social influence drives both offline and online human behavior. It pervades cultural markets, and manifests itself in the adoption of scientific and technical innovations as well as the spread of social practices. Prior empirical work on the diffusion of innovations in spatial regions or social networks has largely focused on the spread of one particular technology among a subset of all potential adopters. Here we choose an online context that allows us to study social influence processes by tracking the popularity of a complete set of applications installed by the user population of a social networking site, thus capturing the behavior of all individuals who can influence each other in this context. By extending standard fluctuation scaling methods, we analyze the collective behavior induced by 100 million application installations, and show that two distinct regimes of behavior emerge in the system. Once applications cross a particular threshold of popularity, social influence processes induce highly correlated adoption behavior among the users, which propels some of the applications to extraordinary levels of popularity. Below this threshold, the collective effect of social influence appears to vanish almost entirely, in a manner that has not been observed in the offline world. Our results demonstrate that even when external signals are absent, social influence can spontaneously assume an on-off nature in a digital environment. It remains to be seen whether a similar outcome could be observed in the offline world if equivalent experimental conditions could be replicated.