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Using a high-throughput approach based on density functional theory, we perform an extensive study of possible ABX3 perovskites, where X is a non-metal and A and B span a large portion of the periodic table. We calculate the ternary phase diagram for each composition and we discuss the thermodynamic stability of perovskite phases. We find a large number of ABX3 perovskites, which are still absent from available databases, and which are stable with respect to decomposition into known ternary, binary or elementary phases. For these structures, we then calculate electronic band gaps, hole effective masses, and the spontaneous ferroelectric and magnetic polarization, which are relevant material properties for a number of specific applications in photovoltaics, transparent contacts, piezoelectrics, and magnetoelectrics. Some of our novel perovskites exhibit promising properties for applications.