How does the public want a COVID-19 vaccine to be allocated? We conducted a conjoint experiment asking 15,536 adults in 13 countries to evaluate 248,576 profiles of potential vaccine recipients who varied randomly on five attributes. Our sample includes diverse countries from all continents. The results suggest that in addition to giving priority to health workers and to those at high risk, the public favors giving priority to a broad range of key workers and to those with lower income. These preferences are similar across respondents of different education levels, incomes, and political ideologies, as well as across most surveyed countries. The public favored COVID-19 vaccines being allocated solely via government programs but were highly polarized in some developed countries on whether taking a vaccine should be mandatory. There is a consensus among the public on many aspects of COVID-19 vaccination, which needs to be taken into account when developing and communicating rollout strategies.