Cell polarization, the spatial self-organization of key molecules asymmetrically at distinct poles, is critical for cell growth, differentiation, and migration in diverse cell types. Previous studies have largely focused on a few network architectures that can achieve polarity and explored how they explain observed behavior. Here, we computationally explored the full space of one- and two-node signaling network architectures in an unbiased manner using coarse-grained representations, in order to elucidate the core design principles of cell polarity. We found three minimal motifs - positive feedback, mutual inhibition, and presence of a self-enhancing inhibitor - that can self-organize polarity and compared their robustness to variations in component concentrations, diffusion constants, and regulation strengths. Combining these motifs into more complex networks allowed for polarity over a wider range of parameters. Robust polarity is in fact best achieved by combining positive feedback with mutual inhibition, as has been observed in many well-studied biological polarity pathways. Such topologies, likely the result of an evolutionary process, can also serve as blueprints for synthetic biologists.