Civil unrest is a powerful form of collective human dynamics, which has led to major transitions of societies in modern history. The study of collective human dynamics, including collective aggression, has been the focus of much discussion in the context of modeling and identification of universal patterns of behavior. In contrast, the possibility that civil unrest activities, across countries and over long time periods, are governed by universal mechanisms has not been explored. Here, records of civil unrest of 170 countries during the period 1919–2008 are analyzed. It is demonstrated that the distributions of the number of unrest events per year are robustly reproduced by a nonlinear, spatially extended dynamical model, which reflects the spread of civil disorder between geographic regions connected through social and communication networks. The results also expose the similarity between global social instability and the dynamics of natural hazards and epidemics.