Copy number variation (CNV) contributes to the genetic basis of disease and has significantly restructured the genomes of humans and great apes. The diversity and rate of this process, however, has not been extensively explored among the great ape lineages. We analyzed 97 deeply sequenced great ape and human genomes and estimate that 16% (469 Mbp) of the hominid genome has been affected by recent copy number changes. We identify a comprehensive set of fixed gene deletion (n=340) and duplication (n=405) events as well as more than 13.5 Mbp of genomic sequence that has been specifically lost on the human lineage over the last 16 million years of evolution. We compared the diversity and rates of copy number and single nucleotide variation across different time points of the hominid phylogeny. We find that CNV diversity partially correlates with single nucleotide polymorphism diversity (r2=0.5) and recapitulates the phylogeny of apes with few exceptions. Duplications significantly outpace deletions (2.8-fold), especially along ancestral African great ape branches. The load of segregating duplications remains significantly higher in bonobos, Western chimpanzees, and Sumatran orangutans - populations that have experienced recent genetic bottlenecks (P=0.0014, 0.02 and 0.0088, respectively). We find that the rate of fixed deletion has been more clocklike with the exception of the chimpanzee lineage where we observe a twofold increase in the chimpanzee-bonobo ancestor (P=4.79 X 10-9) and evidence of increased deletion load among Western chimpanzees (P=0.002). The latter includes the first evidence of a genomic disorder in a chimpanzee with features resembling Smith-Magenis syndrome mediated by a chimpanzee-specific increase in segmental duplication complexity. We hypothesize that demographic effects, such as bottlenecks, have contributed to larger and more gene-rich segments being deleted in the chimpanzee lineage and that this effect, more generally, may account for episodic bursts in CNV during hominid evolution.