A biological system is robust to mutations if it continues to function after genetic changes in its parts. Such robustness is pervasive on different levels of biological organization, from macromolecules to genetic networks and whole organisms. I here ask which of two possible causes of such robustness are more important on a genome-wide scale, for systems whose parts are genes, such as metabolic and genetic networks. The first of the two causes is redundancy of a system's parts: A gene may be dispensable if the genome contains redundant, back-up copies of the gene. The second cause, distributed robustness, is more poorly understood. It emerges from the distributed nature of many biological systems, where many (and different) parts contribute to system functions. I will here discuss evidence suggesting that distributed robustness is equally or more important for mutational robustness than gene redundancy. This evidence comes from the functional divergence of redundant genes, as well as from large-scale gene deletion studies. I also ask whether one can quantify the extent to which redundancy or distributed robustness contribute to mutational robustness.