The gene regulatory network (GRN) is the central decision-making module of cells. We show that experimentally derived GRNs of diverse prokaryotes and eukaryotes all obey severe topological constraints that allow stable network responses under arbitrary perturbations, including the random addition of new regulatory connections. We call this network structure, which confers such profound stability, Buffered Qualitative Stability (BQS). BQS makes strong and diverse predictions about network properties. All of these predictions are verified. Using BQS, we also highlight possible mechanism of antibiotic resistance and cancer development.