Copy number variants (CNVs) account for a major proportion of human genetic polymorphism and have been predicted to have an important role in genetic susceptibility to common disease. To address this we undertook a large, direct genome-wide study of association between CNVs and eight common human diseases. Using a purpose-designed array we typed ∼19,000 individuals into distinct copy-number classes at 3,432 polymorphic CNVs, including an estimated ∼50% of all common CNVs larger than 500 base pairs. We identified several biological artefacts that lead to false-positive associations, including systematic CNV differences between DNAs derived from blood and cell lines. Association testing and follow-up replication analyses confirmed three loci where CNVs were associated with disease—IRGM for Crohn’s disease, HLA for Crohn’s disease, rheumatoid arthritis and type 1 diabetes, and TSPAN8 for type 2 diabetes—although in each case the locus had previously been identified in single nucleotide polymorphism (SNP)-based studies, reflecting our observation that most common CNVs that are well-typed on our array are well tagged by SNPs and so have been indirectly explored through SNP studies. We conclude that common CNVs that can be typed on existing platforms are unlikely to contribute greatly to the genetic basis of common human diseases.