Evolution is typically thought to proceed through divergence of genes, proteins, and ultimately phenotypes1-3. However, similar traits might also evolve convergently in unrelated taxa due to similar selection pressures4,5. Adaptive phenotypic convergence is widespread in nature, and recent results from a handful of genes have suggested that this phenomenon is powerful enough to also drive recurrent evolution at the sequence level6-9. Where homoplasious substitutions do occur these have long been considered the result of neutral processes. However, recent studies have demonstrated that adaptive convergent sequence evolution can be detected in vertebrates using statistical methods that model parallel evolution9,10 although the extent to which sequence convergence between genera occurs across genomes is unknown. Here we analyse genomic sequence data in mammals that have independently evolved echolocation and show for the first time that convergence is not a rare process restricted to a handful of loci but is instead widespread, continuously distributed and commonly driven by natural selection acting on a small number of sites per locus. Systematic analyses of convergent sequence evolution in 805,053 amino acids within 2,326 orthologous coding gene sequences compared across 22 mammals (including four new bat genomes) revealed signatures consistent with convergence in nearly 200 loci. Strong and significant support for convergence among bats and the dolphin was seen in numerous genes linked to hearing or deafness, consistent with an involvement in echolocation. Surprisingly we also found convergence in many genes linked to vision: the convergent signal of many sensory genes was robustly correlated with the strength of natural selection. This first attempt to detect genome-wide convergent sequence evolution across divergent taxa reveals the phenomenon to be much more pervasive than previously recognised.