The objective of this study was to determine the correlation between adherence to cancer screening programs and earlier diagnosis of the 14 most common types of cancers in the adult population, before and during the COVID-19 pandemic. National data concerning number of admissions and operations in Italy for adult patients admitted with oncologic problems during the COVID-19 pandemic (2020 to 2022) and in the pre-pandemic period (2015 to 2019) were analyzed. We selected 14 types of cancer that present the most common indications for surgery in Italy. This study included 1,365,000 adult patients who had surgery for the 14 most common types of cancer in the period 2015-2022, and interviews concerning adherence rates to screening for breast, colorectal, and cervical cancer were conducted for 133,455 individuals. A higher decrease in the number of operations for the 14 types of cancer (-45%) was registered during the first three acute phases of the pandemic, and it was more evident for screenable cancers like breast, colorectal, and cervical cancer (p < 0.001). During the first year of the COVID-19 pandemic, the number of screened individuals for breast, colorectal, and cervical cancer decreased by 33.8% (from 7,507,893 to 4,969,000) and the number of diagnoses and operations for these three types of cancer decreased by 10.5% (from 107,656 to 96,405). The increase and return to normality of the number of screened individuals in the last year of the pandemic (2022) and in the first post-pandemic year (2023) was associated with a return to the pre-pandemic levels of diagnoses and operations. The adherence rates were lower for individuals living in rural areas, with low socio-economic status, and unmarried persons; however, the most statistically significant factor for reduced adherence was a lower level of educational attainment. Free screening through nationally organized programs reduced social disparities. There were no significant differences between the pre-pandemic and pandemic periods for several types of cancers (stomach, esophagus, pancreas, liver) that are diagnosed for the occurrence of symptoms and for which nationally organized programs might increase the possibility of earlier diagnosis and improved clinical outcomes. Education, information, and appropriate expenditure for preventive care have the potential to reduce cancer mortality. Nationally organized screening programs for several types of cancers, which are often detected for the occurrence of symptoms, may increase the possibility of diagnosis at earlier stages.