Understanding the determinants of COVID-19 vaccine uptake is important to inform policy decisions and plan vaccination campaigns. The aims of this research were to: (1) explore the individual- and country-level determinants of intentions to be vaccinated against SARS-CoV-2, and (2) examine worldwide variation in vaccination intentions. This cross-sectional online survey was conducted during the first wave of the pandemic, involving 6697 respondents across 20 countries. Results showed that 72.9% of participants reported positive intentions to be vaccinated against COVID-19, whereas 16.8% were undecided, and 10.3% reported they would not be vaccinated. At the individual level, prosociality was a significant positive predictor of vaccination intentions, whereas generic beliefs in conspiracy theories and religiosity were negative predictors. Country-level determinants, including cultural dimensions of individualism/collectivism and power distance, were not significant predictors of vaccination intentions. Altogether, this study identifies individual-level predictors that are common across multiple countries, provides further evidence on the importance of combating conspiracy theories, involving religious institutions in vaccination campaigns, and stimulating prosocial motives to encourage vaccine uptake.