SNP genotyping has emerged as a technology to incorporate copy number variants (CNVs) into genetic analyses of human traits. However, the extent to which SNP platforms accurately capture CNVs remains unclear. Using independent, sequence-based CNV maps, we find that commonly used SNP platforms have limited or no probe coverage for a large fraction of CNVs. Despite this, in 9 samples we inferred 368 CNVs using Illumina SNP genotyping data and experimentally validated over two-thirds of these. We also developed a method (SNP-Conditional Mixture Modeling, SCIMM) to robustly genotype deletions using as few as two SNP probes. We find that HapMap SNPs are strongly correlated with 82% of common deletions, but the newest SNP platforms effectively tag about 50%. We conclude that currently available genome-wide SNP assays can capture CNVs accurately, but improvements in array designs, particularly in duplicated sequences, are necessary to facilitate more comprehensive analyses of genomic variation.