The mechanical properties of ordinary materials degrade substantially with reduced density because their structural elements bend under applied load. We report a class of microarchitected materials that maintain a nearly constant stiffness per unit mass density, even at ultralow density. This performance derives from a network of nearly isotropic microscale unit cells with high structural connectivity and nanoscale features, whose structural members are designed to carry loads in tension or compression. Production of these microlattices, with polymers, metals, or ceramics as constituent materials, is made possible by projection microstereolithography (an additive micromanufacturing technique) combined with nanoscale coating and postprocessing. We found that these materials exhibit ultrastiff properties across more than three orders of magnitude in density, regardless of the constituent material.