Aim: The aim of the study was to investigate the incidence of human papillomavirus (HPV)-associated cancers in Denmark between 1978 and 2011, estimate the current absolute annual number (burden) of HPV-associated cancers (HPVaCa) and their precancerous lesions, and assess whether there is socioeconomic inequality in the risk of HPV-associated cancers. Methods: From four nationwide population-based registries, information was collected on HPVaCa diagnosed during 1978–2011 and age-standardised incidence rate for each site by calendar year and birth cohort was calculated. Furthermore, the current annual burden of HPVaCa and severe precancerous lesions was estimated. Incidence rate ratios and corresponding 95% confidence intervals for HPVaCa were calculated according to socioeconomic status. Results: The age-standardised incidence rate of HPV-associated cancers for the two sexes converged during the study period, and almost identical incidence rates were seen for women and men in the youngest birth cohorts. The current burden of HPV-associated lesions amounted to more than 5000 cases, the vast majority (85%) being severe precancerous lesions. The highest risk for HPV-associated cancers was associated with lower socioeconomic status. Conclusions: The burden of HPV-associated cancers among men will likely surpass that among women in the near future if the incidence trends continue. As many of these cancers and their precancerous lesions are associated with HPV type 16, a substantial proportion of cases are, in theory, preventable by the currently available vaccines.