With the number of sequenced genomes now over one hundred, and the availability of rough functional annotations for a substantial proportion of their genes, it has become possible to study the statistics of gene content across genomes. Here I show that, for many high-level functional categories, the number of genes in the category scales as a power-law in the total number of genes in the genome. The occurrence of such scaling laws can be explained with a simple theoretical model, and this model suggests that the exponents of the observed scaling laws correspond to universal constants of the evolutionary process. I discuss some consequences of these scaling laws for our understanding of organism design.