Identity-by-descent (IBD) mapping tests whether cases share more segments of IBD around a putative causal variant than do controls. These segments of IBD can be accurately detected from genome-wide SNP data. We investigate the power of IBD mapping relative to that of SNP association testing for genome-wide case-control SNP data. Our focus is particularly on rare variants, as these tend to be more recent and hence more likely to have recent shared ancestry. We simulate data from both large and small populations and find that the relative performance of IBD mapping and SNP association testing depends on population demographic history and the strength of selection against causal variants. We also present an IBD mapping analysis of a type 1 diabetes data set. In those data we find that we can detect association only with the HLA region using IBD mapping. Overall, our results suggest that IBD mapping may have higher power than association analysis of SNP data when multiple rare causal variants are clustered within a gene. However, for outbred populations, very large sample sizes may be required for genome-wide significance unless the causal variants have strong effects.