OpenStreetMap (OSM) has evolved as a popular dataset for global urban analyses, such as assessing progress towards the Sustainable Development Goals. However, many analyses do not account for the uneven spatial coverage of existing data. We employ a machine-learning model to infer the completeness of OSM building stock data for 13,189 urban agglomerations worldwide. For 1,848 urban centres (16% of the urban population), OSM building footprint data exceeds 80% completeness, but completeness remains lower than 20% for 9,163 cities (48% of the urban population). Although OSM data inequalities have recently receded, partially as a result of humanitarian mapping efforts, a complex unequal pattern of spatial biases remains, which vary across various human development index groups, population sizes and geographic regions. Based on these results, we provide recommendations for data producers and urban analysts to manage the uneven coverage of OSM data, as well as a framework to support the assessment of completeness biases.