Pre-existing T cell immunity to SARS-CoV-2 in individuals without prior exposure to SARS-CoV-2 has been reported in several studies. While emerging evidence hints toward prior exposure to common-cold human coronaviruses (HCoV), the extent of- and conditions for- cross-protective immunity between SARS-CoV-2 and HCoVs remain open. Here, by leveraging a comprehensive pool of publicly available functionally evaluated SARS-CoV-2 peptides, we report 126 immunogenic SARS-CoV-2 peptides with high sequence similarity to 285 MHC-presented target peptides from at least one of four HCoV, thus providing a map describing the landscape of SARS-CoV-2 shared and private immunogenic peptides with functionally validated T cell responses. Using this map, we show that while SARS-CoV-2 immunogenic peptides in general exhibit higher level of dissimilarity to both self-proteome and -microbiomes, there exist several SARS-CoV-2 immunogenic peptides with high similarity to various human protein coding genes, some of which have been reported to have elevated expression in severe COVID-19 patients. We then combine our map with a SARS-CoV-2-specific TCR repertoire data from COVID-19 patients and healthy controls and show that whereas the public repertoire for the majority of convalescent patients are dominated by TCRs cognate to private SARS-CoV-2 peptides, for a subset of patients, more than 50% of their public repertoires that show reactivity to SARS-CoV-2, consist of TCRs cognate to shared SARS-CoV-2-HCoV peptides. Further analyses suggest that the skewed distribution of TCRs cognate to shared and private peptides in COVID-19 patients is likely to be HLA-dependent. Finally, by utilising the global prevalence of HLA alleles, we provide 10 peptides with known cognate TCRs that are conserved across SARS-CoV-2 and multiple human coronaviruses and are predicted to be recognised by a high proportion of the global population. Overall, our work indicates the potential for HCoV-SARS-CoV-2 reactive CD8+ T cells, which is likely dependent on differences in HLA-coding genes among individuals. These findings may have important implications for COVID-19 heterogeneity and vaccine-induced immune responses as well as robustness of immunity to SARS-CoV-2 and its variants.