House mice (Mus musculus) have spread globally as a result of their commensal relationship with humans. In the form of laboratory strains, both inbred and outbred, they are also among the most widely-used model organisms in biomedical research. Although the general outlines of house mouse dispersal and population structure are well known, details have been obscured by either limited sample size or small numbers of markers. Here we examine ancestry, population structure, and inbreeding using SNP microarray genotypes in a cohort of 814 wild mice spanning five continents and all major subspecies of Mus, with a focus on M. m. domesticus. We find that the major axis of genetic variation in M. m. domesticus is a south-to-north gradient within Europe and the Mediterranean. The dominant ancestry component in North America, Australia, New Zealand, and various small offshore islands is of northern European origin. Next, we show that inbreeding is surprisingly pervasive and highly variable, even between nearby populations. By inspecting the length distribution of homozygous segments in individual genomes, we find that inbreeding in commensal populations is mostly due to consanguinity. Our results offer new insight into the natural history of an important model organism for medicine and evolutionary biology.