Background: The Coronavirus Disease 2019 (COVID-19) pandemic has highlighted the need for preventive medicine and vaccinology to be paralleled to eliminate COVID-19 cases. Methods: A web-based questionnaire was disseminated through social media in the late November assessing the factors that may have influenced the final response to vaccination against COVID-19 in vaccinated and non-vaccinated Greek people. Results: Women, the younger generations, and university graduates were more likely to accept vaccination, whereas men, those with a basic education level, and the older generation showed a hesitance to the vaccine against COVID-19. About half of the vaccinated participants were influenced in their final decision mainly by being informed from the internet (50.4%), their work (51.7%), and social life (53,1%) while half of the non-vaccinated individuals were mostly influenced by keeping updated from the internet (55.5%) and by government policies (51.3%). COVID-19 risk (OR 2.511; CI 2.149–2.934; p = 0.000), frequent vaccinations for emerging pathogens (OR 14.022; CI 11.998-16.389), and social life (OR 2.828; CI 2.417–3.309; p = 0.000) had a significant impact on people’s positive response to vaccination against COVID-19. Conclusions: Monitoring and assessing the influence factors for the response to vaccination can be favourable strategies to further manage societal vaccination rates.