Information avalanches in social media are typically studied in a similar fashion as avalanches of neuronal activity in the brain. Whereas a large body of literature reveals substantial agreement about the existence of a unique process characterizing neuronal activity across organisms, the dynamics of information in online social media is far less understood. Statistical laws of information avalanches are found in previous studies to be not robust across systems, and radically different processes are used to represent plausible driving mechanisms for information propagation. Here, we analyze almost 1 billion time-stamped events collected from a multitude of online platforms -- including Telegram, Twitter and Weibo -- over observation windows longer than 10 years to show that the propagation of information in social media is a universal and critical process. Universality arises from the observation of identical macroscopic patterns across platforms, irrespective of the details of the specific system at hand. Critical behavior is deduced from the power-law distributions, and corresponding hyperscaling relations, characterizing size and duration of avalanches of information. Neuronal activity may be modeled as a simple contagion process, where only a single exposure to activity may be sufficient for its diffusion. On the contrary, statistical testing on our data indicates that a mixture of simple and complex contagion, where involvement of an individual requires exposure from multiple acquaintances, characterizes the propagation of information in social media. We show that the complexity of the process is correlated with the semantic content of the information that is propagated. Conversational topics about music, movies and TV shows tend to propagate as simple contagion processes, whereas controversial discussions on political/societal themes obey the rules of complex contagion.