Proton conduction is a fundamental process in biology and in devices such as proton exchange membrane fuel cells. To maximize proton conduction, three-dimensional conduction pathways are preferred over one-dimensional pathways, which prevent conduction in two dimensions. Many crystalline porous solids to date show one-dimensional proton conduction. Here we report porous molecular cages with proton conductivities (up to 10(-3) S cm(-1) at high relative humidity) that compete with extended metal-organic frameworks. The structure of the organic cage imposes a conduction pathway that is necessarily three-dimensional. The cage molecules also promote proton transfer by confining the water molecules while being sufficiently flexible to allow hydrogen bond reorganization. The proton conduction is explained at the molecular level through a combination of proton conductivity measurements, crystallography, molecular simulations and quasi-elastic neutron scattering. These results provide a starting point for high-temperature, anhydrous proton conductors through inclusion of guests other than water in the cage pores.