The domestic dog is becoming an increasingly valuable model species in medical genetics, showing particular promise to advance our understanding of cancer and orthopaedic disease. Here we undertake the largest canine genome-wide association study to date, with a panel of over 4,200 dogs genotyped at 180,000 markers, to accelerate mapping efforts. For complex diseases, we identify loci significantly associated with hip dysplasia, elbow dysplasia, idiopathic epilepsy, lymphoma, mast cell tumour and granulomatous colitis; for morphological traits, we report three novel quantitative trait loci that influence body size and one that influences fur length and shedding. Using simulation studies, we show that modestly larger sample sizes and denser marker sets will be sufficient to identify most moderate- to large-effect complex disease loci. This proposed design will enable efficient mapping of canine complex diseases, most of which have human homologues, using far fewer samples than required in human studies.