Copy number variants (CNVs) account for a major proportion of human genetic polymorphism and have been predicted to play 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 500bp. 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, though in each case the locus had previously been identified in SNP-based studies, reflecting our observation that the majority of common CNVs which 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 which can be typed on existing platforms are unlikely to contribute greatly to the genetic basis of common human diseases.