A central goal in cancer genomics is to identify the somatic alterations that underpin tumor initiation and progression. While commonly mutated cancer genes are readily identifiable, those that are rarely mutated across samples are difficult to distinguish from the large numbers of other infrequently mutated genes. We introduce a method, nCOP, that considers per-individual mutational profiles within the context of protein-protein interaction networks in order to identify small connected subnetworks of genes that, while not individually frequently mutated, comprise pathways that are altered across (i.e., "cover") a large fraction of individuals. By analyzing 6,038 samples across 24 different cancer types, we demonstrate that nCOP is highly effective in identifying cancer genes, including those with low mutation frequencies. Overall, our work demonstrates that combining per-individual mutational information with interaction networks is a powerful approach for tackling the mutational heterogeneity observed across cancers.