Selective breeding of dogs has resulted in repeated artificial selection on breed-specific morphological phenotypes. A number of quantitative trait loci associated with these phenotypes have been identified in genetic mapping studies. We analyzed the population genomic signatures observed around the causal mutations for 12 of these loci in 25 dog breeds, for which we genotyped 25 individuals in each breed. By measuring the population frequencies of the causal mutations in each breed, we identified those breeds in which specific mutations most likely experienced positive selection. These instances were then used as positive controls for assessing the performance of popular statistics to detect selection from population genomic data. We found that artificial selection during dog domestication has left characteristic signatures in the haplotype and nucleotide polymorphism patterns around selected loci that can be detected in the genotype data from a single population sample. However, the sensitivity and accuracy at which such signatures were detected varied widely between loci, the particular statistic used, and the choice of analysis parameters. We observed examples of both hard and soft selective sweeps and detected strong selective events that removed genetic diversity almost entirely over regions >10 Mbp. Our study demonstrates the power and limitations of selection scans in populations with high levels of linkage disequilibrium due to severe founder effects and recent population bottlenecks.