The type I interferon (IFN) response protects cells from viral infection by inducing hundreds of interferon-stimulated genes (ISGs), some of which encode direct antiviral effectors. Recent screening studies have begun to catalogue ISGs with antiviral activity against several RNA and DNA viruses. However, antiviral ISG specificity across multiple distinct classes of viruses remains largely unexplored. Here we used an ectopic expression assay to screen a library of more than 350 human ISGs for effects on 14 viruses representing 7 families and 11 genera. We show that 47 genes inhibit one or more viruses, and 25 genes enhance virus infectivity. Comparative analysis reveals that the screened ISGs target positive-sense single-stranded RNA viruses more effectively than negative-sense single-stranded RNA viruses. Gene clustering highlights the cytosolic DNA sensor cyclic GMP-AMP synthase (cGAS, also known as MB21D1) as a gene whose expression also broadly inhibits several RNA viruses. In vitro, lentiviral delivery of enzymatically active cGAS triggers a STING-dependent, IRF3-mediated antiviral program that functions independently of canonical IFN/STAT1 signalling. In vivo, genetic ablation of murine cGAS reveals its requirement in the antiviral response to two DNA viruses, and an unappreciated contribution to the innate control of an RNA virus. These studies uncover new paradigms for the preferential specificity of IFN-mediated antiviral pathways spanning several virus families.