Copy number variation (CNV) is a key source of genetic diversity, but a comprehensive understanding of its phenotypic effect is only beginning to emerge. We have generated a CNV map in wild mice and classical inbred strains. Genome-wide expression data from six major organs show not only that expression of genes within CNVs tend to correlate with copy number changes, but also that CNVs influence the expression of genes in their vicinity, an effect that extends up to half a megabase. Genes within CNVs show lower expression and more specific spatial expression patterns than genes mapping elsewhere. Our analyses reveal differential constraint on copy number changes of genes expressed in different tissues. Dosage alterations of brain-expressed genes are less frequent than those of other genes and are buffered by tighter transcriptional regulation. Our study provides initial evidence that CNVs shape tissue transcriptomes on a global scale.