Living systems naturally exhibit internal driving: active, molecular processes drive non-equilibrium phenomena such as metabolism or migration. Active gels constitute a fascinating class of internally driven matter, in which molecular motors exert localized stresses inside polymer networks. There is evidence that network crosslinking is required to allow motors to induce macroscopic contraction. Yet a quantitative understanding of how network connectivity enables contraction is lacking. Here we show experimentally that myosin motors contract crosslinked actin polymer networks to clusters with a scale-free size distribution. This critical behaviour occurs over an unexpectedly broad range of crosslink concentrations. To understand this robustness, we developed a quantitative model of contractile networks that takes into account network restructuring: motors reduce connectivity by forcing crosslinks to unbind. Paradoxically, to coordinate global contractions, motor activity should be low. Otherwise, motors drive initially well-connected networks to a critical state where ruptures form across the entire network. © 2013 Macmillan Publishers Limited.