Tandemly repeating DNA elements known as satellite DNA occupy significant portions of Drosophila genomes. As they are prone to cause genomic instability through non-allelic exchange, they are predominantly sequestered in the repressive heterochromatin near the centromeres and telomeres, as well as on the Y where they accumulate as the chromosome degenerates. Interestingly, the types and abundances of satellites vary dramatically between closely related species, suggesting that they are turning-over at high rates. Yet they are often ignored in genome assemblies due to low-sequence complexity and repetitiveness, leading to poor understanding of the evolutionary dynamics underlying the observed rapid changes. Here, we identify and quantify simple satellites using the program k-Seek on whole genome sequences of nine Drosophila species, spanning 40 million years of evolution. We find that very few satellites are shared across species, consistent with the expectation of rapid turn-over. However, when we determined the gains and losses of satellite DNA along the Drosophila phylogeny based on parsimony, we found that most of the interspecific differences are due to lineage-specific gains of satellites; loss events, in comparison, are extremely rare. The rates of gain also differ greatly among lineages, as some species appear to have acquired few to no satellites, while others, including those in the melanogaster complex, have accumulated large numbers in a relatively short time. To separately test for satellite age, we identified heterogeneity in satellites caused by mutations and found that older satellites indeed have significantly more indels than younger satellites. In addition, we identified Y-linked satellites via enrichment in males, and found that some Ys are, unexpectedly, satellite-poor, such as the young neo-Ys in the species of the obscura group. Our results indicate that within Drosophila species, the vast differences in satellite DNA are predominantly driven by rapid accumulations in only some species.