Understanding the immune response to severe acute respiratory syndrome coronavirus (SARS-CoV-2) is critical to overcome the current coronavirus disease (COVID-19) pandemic. Efforts are being made to understand the potential cross-protective immunity of memory T cells, induced by prior encounters with seasonal coronaviruses, in providing protection against severe COVID-19. In this study we assessed T-cell responses directed against highly conserved regions of SARS-CoV-2. Epitope mapping revealed 16 CD8+ T-cell epitopes across the nucleocapsid (N), spike (S) and ORF3a proteins of SARS-CoV-2 and five CD8+ T-cell epitopes encoded within the highly conserved regions of the ORF1ab polyprotein of SARS-CoV-2. Comparative sequence analysis showed high conservation of SARS-CoV-2 ORF1ab T-cell epitopes in seasonal coronaviruses. Paradoxically, the immune responses directed against the conserved ORF1ab epitopes were infrequent and subdominant in both convalescent and unexposed participants. This subdominant immune response was consistent with a low abundance of ORF1ab encoded proteins in SARS-CoV-2 infected cells. Overall, these observations suggest that while cross-reactive CD8+ T cells likely exist in unexposed individuals, they are not common and therefore are unlikely to play a significant role in providing broad pre-existing immunity in the community.