Single-walled carbon nanotubes (SWNT) were reported to have record high hydrogen storage capacities at room temperature, indicating an interaction between hydrogen and carbon matrix that is stronger than known before. Here we present a study of the interaction of hydrogen with activated charcoal, carbon nanofibers, and SWNT that disproves these earlier reports. The hydrogen storage capacity of these materials correlates with the surface area of the material, the activated charcoal having the largest. The SWNT appear to have a relatively low accessible surface area due to bundling of the tubes; the hydrogen does not enter the voids between the tubes in the bundles. Pressure–temperature curves were used to estimate the interaction potential, which was found to be 580±60 K. Hydrogen gas was adsorbed in amounts up to 2 wt % only at low temperatures. Molecular rotations observed with neutron scattering indicate that molecular hydrogen is present, and no significant difference was found between the hydrogen molecules adsorbed in the different investigated materials. Results from density functional calculations show molecular hydrogen bonding to an aromatic CC bond that is present in the materials investigated. The claims of high storage capacities of SWNT related to their characteristic morphology are unjustified.