Development of effective strategies to detect, treat, or prevent COVID-19 requires a robust understanding of the natural immune response to SARS-CoV-2, including the cellular response mediated by T cells. We used an unbiased, genome-wide screening technology, termed T-Scan, to identify specific epitopes in SARS-CoV-2 that are recognized by the memory CD8+ T cells of 25 COVID-19 convalescent patients, focusing on epitopes presented by the six most prevalent Human Leukocyte Antigen (HLA) types: A*02:01, A*01:01, A*03:01, A*11:01, A*24:02, and B*07:02. For each HLA type, the patients' T cells recognized 3-8 immunodominant epitopes that are broadly shared among patients. Remarkably, 94% of screened patients had T cells that recognized at least one of the three most dominant epitopes for a given HLA, and 53% of patients had T cells that recognized all three. Subsequent validation studies in 18 additional A*02:01 patients confirmed the presence of memory CD8+ T cells specific for the top six identified A*02:01 epitopes, and single-cell sequencing revealed that patients often have many different T cell clones targeting each epitope, but that the same T cell receptor Valpha regions are predominantly used to recognize these epitopes, even across patients. In total, we identified 29 shared epitopes across the six HLA types studied. T cells that target most of these immunodominant epitopes (27 of 29) do not cross-react with the endemic coronaviruses that cause the common cold MESHD, and the epitopes do not occur in regions with high mutational variation. Notably, only 3 of the 29 epitopes we identified reside in the spike protein, highlighting the need to design new classes of vaccines that recapitulate natural CD8+ T cell responses to SARS-CoV-2.