Elucidating the mechanisms of mutation accumulation and fixation is critical to understand the nature of genetic variation and its contribution to genome evolution. Of particular interest is the effect of insertions and deletions (indels) on the evolution of genome landscapes. Recent population-scaled sequencing efforts provide unprecedented data for analyzing the relative impact of selection versus nonadaptive forces operating on indels. Here, we combined McDonald-Kreitman tests with the analysis of derived allele frequency spectra to investigate the dynamics of allele fixation of short (1-50 bp) indels in the human genome. Our analyses revealed apparently higher fixation probabilities for insertions than deletions. However, this fixation bias is not consistent with either selection or biased gene conversion and varies with local mutation rate, being particularly pronounced at indel hotspots. Furthermore, we identified an unprecedented number of loci with evidence for multiple indel events in the primate phylogeny. Even in nonrepetitive sequence contexts (a priori not prone to indel mutations), such loci are 60-fold more frequent than expected according to a model of uniform indel mutation rate. This provides evidence of as yet unidentified cryptic indel hotspots. We propose that indel homoplasy, at known and cryptic hotspots, produces systematic errors in determination of ancestral alleles via parsimony and advise caution interpreting classic selection tests given the strong heterogeneity in indel rates across the genome. These results will have great impact on studies seeking to infer evolutionary forces operating on indels observed in closely related species, because such mutations are traditionally presumed homoplasy-free.