The H₂ capacities of a diverse set of 918,734 metal-organic frameworks (MOFs) sourced from 19 databases is predicted via machine learning (ML). Using only 7 structural features as input, ML identifies 8,282 MOFs with the potential to exceed the capacities of state-of-the-art materials. The identified MOFs are predominantly hypothetical compounds having low densities (<0.31 g cm⁻³) in combination with high surface areas (>5,300 m² g⁻¹), void fractions (∼0.90), and pore volumes (>3.3 cm³ g⁻¹). The relative importance of the input features are characterized, and dependencies on the ML algorithm and training set size are quantified. The most important features for predicting H₂ uptake are pore volume (for gravimetric capacity) and void fraction (for volumetric capacity). The ML models are available on the web, allowing for rapid and accurate predictions of the hydrogen capacities of MOFs from limited structural data; the simplest models require only a single crystallographic feature.