Genome-wide scans for selection have identified multiple regions of the human genome as being targeted by positive selection. However, only a small proportion has been replicated across studies, and the prevalence of positive selection as a mechanism of adaptive change in humans remains controversial. Here we explore the power of two haplotype-based statistics--the integrated haplotype score (iHS) and the Derived Intraallelic Nucleotide Diversity (DIND) test--in the context of next-generation sequencing data, and evaluate their robustness to demography and other selection modes. We show that these statistics are both powerful for the detection of recent positive selection, regardless of population history, and robust to variation in coverage, with DIND being insensitive to very low coverage. We apply these statistics to whole-genome sequence data sets from the 1000 Genomes Project and Complete Genomics. We found that putative targets of selection were highly significantly enriched in genic and nonsynonymous single nucleotide polymorphisms, and that DIND was more powerful than iHS in the context of small sample sizes, low-quality genotype calling, or poor coverage. As we excluded genomic confounders and alternative selection models, such as background selection, the observed enrichment attests to the action of recent, strong positive selection. Further support to the adaptive significance of these genomic regions came from their enrichment in functional variants detected by genome-wide association studies, informing the relationship between past selection and current benign and disease-related phenotypic variation. Our results indicate that hard sweeps targeting low-frequency standing variation have played a moderate, albeit significant, role in recent human evolution.