Recent advances in high‐throughput technologies are bringing the study of empirical genotype‐phenotype (GP) maps to the fore. Here, we use data from protein‐binding microarrays to study an empirical GP map of transcription factor (TF) ‐binding preferences. In this map, each genotype is a DNA sequence. The phenotype of this DNA sequence is its ability to bind one or more TFs. We study this GP map using genotype networks, in which nodes represent genotypes with the same phenotype, and edges connect nodes if their genotypes differ by a single small mutation. We describe the structure and arrangement of genotype networks within the space of all possible binding sites for 525 TFs from three eukaryotic species encompassing three kingdoms of life (animal, plant, and fungi). We thus provide a high‐resolution depiction of the architecture of an empirical GP map. Among a number of findings, we show that these genotype networks are “small‐world” and assortative, and that they ubiquitously overlap and interface with one another. We also use polymorphism data from Arabidopsis thaliana to show how genotype network structure influences the evolution of TF‐binding sites in vivo. We discuss our findings in the context of regulatory evolution.