To face the COVID-19 outbreak, a wide range of non-pharmaceutical interventions (NPIs) aimed at limiting the spread of the virus in communities, such as mask-wearing, hand hygiene, social distancing, travel restrictions, and school closures, were introduced in most countries. Thereafter, a significant reduction of new asymptomatic and symptomatic COVID-19 cases occurred, although there were differences between countries according to the type and duration of the NPIs. In addition, the COVID-19 pandemic has been accompanied by significant variations in the global incidence of diseases due to the most common non-SARS-CoV-2 respiratory viruses and some bacteria. In this narrative review, the epidemiology of the most common non-SARS-CoV-2 respiratory infections during the COVID-19 pandemic is detailed. Moreover, factors that could have had a role in modifying the traditional circulation of respiratory pathogens are discussed. A literature analysis shows that NPIs were the most important cause of the general reduction in the incidence of influenza and respiratory syncytial virus infection in the first year of the pandemic, although the different sensitivity of each virus to NPIs, the type and duration of measures used, as well as the interference among viruses may have played a role in modulating viral circulation. Reasons for the increase in the incidences of Streptococcus pneumoniae and group A Streptococcus infections seem strictly linked to immunity debt and the role played by NPIs in reducing viral infections and limiting bacterial superimposed infections. These results highlight the importance of NPIs during pandemics, the need to monitor the circulation of infectious agents that cause diseases similar to those caused by pandemic agents, and the need to make efforts to improve coverage with available vaccines.