We report detailed peptide-binding affinities between 438 HLA Class I and Class II proteins and complete proteomes of seven pandemic human viruses, including coronaviruses, influenza viruses and HIV-1. We contrast these affinities with HLA allele frequencies across hundreds of human populations worldwide. Statistical modelling shows that peptide-binding affinities classified into four distinct categories depend on the HLA locus but that the type of virus is only a weak predictor, except in the case of HIV-1. Among the strong HLA binders (IC50 ≤ 50), we uncovered 16 alleles (the top ones being A*02:02, B*15:03 and DRB1*01:02) binding more than 1% of peptides derived from all viruses, 9 (top ones including HLA-A*68:01, B*15:25, C*03:02 and DRB1*07:01) binding all viruses except HIV-1, and 15 (top ones A*02:01 and C*14:02) only binding coronaviruses. The frequencies of strongest and weakest HLA peptide binders differ significantly among populations from different geographic regions. In particular, Indigenous peoples of America show both higher frequencies of strongest and lower frequencies of weakest HLA binders. As many HLA proteins are found to be strong binders of peptides derived from distinct viral families, and are hence promiscuous (or generalist), we discuss this result in relation to possible signatures of natural selection on HLA promiscuous alleles due to past pathogenic infections. Our findings are highly relevant for both evolutionary genetics and the development of vaccine therapies. However they should not lead to forget that individual resistance and vulnerability to diseases go beyond the sole HLA allelic affinity and depend on multiple, complex and often unknown biological, environmental and other variables.