There is a limited repertoire of domain families that are duplicated and combined in different ways to form the set of proteins in a genome. Proteins are gene products, and at the level of genes, duplication, recombination, fusion and fission are the processes that produce new genes. We attempt to gain an overview of these processes by studying the evolutionary units in proteins, domains, in the protein sequences of 40 genomes. The domain and superfamily definitions in the Structural Classification of Proteins Database are used, so that we can view all pairs of adjacent domains in genome sequences in terms of their superfamily combinations. We find 783 out of the 859 superfamilies in SCOP in these genomes, and the 783 families occur in 1307 pairwise combinations. Most families are observed in combination with one or two other families, while a few families are very versatile in their combinatorial behaviour; 209 families do not make combinations with other families. This type of pattern can be described as a scale-free network. We also study the N to C-terminal orientation of domain pairs and domain repeats. The phylogenetic distribution of domain combinations is surveyed, to establish the extent of common and kingdom-specific combinations. Of the kingdom-specific combinations, significantly more combinations consist of families present in all three kingdoms than of families present in one or two kingdoms. Hence, we are led to conclude that recombination between common families, as compared to the invention of new families and recombination among these, has also been a major contribution to the evolution of kingdom-specific and species-specific functions in organisms in all three kingdoms. Finally, we compare the set of the domain combinations in the genomes to those in the RCSB Protein Data Bank, and discuss the implications for structural genomics.