Significance How to allocate COVID-19 vaccines is one of the most important decisions currently facing governments. With limited supplies, what is most pressing is deciding who gets priority in the vaccine allocation rollout. Some governments are exploring allowing private purchases of COVID-19 vaccines. Many countries are debating whether COVID-19 vaccines should be mandated. There is little evidence on what policies are preferred by the global public. Our survey of 15,536 adults in 13 countries confirms that priority should be given to health workers and those at high risk but also, to a broad range of key workers and those with lower incomes. The public favors allocating COVID-19 vaccines solely via government programs but was polarized in some countries on mandatory vaccinations.