The adsorption of hydrogen gas into single-walled carbon nanotubes (SWNTs) and idealized carbon slit pores is studied by computer simulation. Hydrogen-hydrogen interactions are modeled with the Silvera-Goldman potential. The Crowell-Brown potential is used to model the hydrogen-carbon interactions. Calculations include adsorption inside the tubes, in the interstitial regions of tube arrays, and on the outside surface of isolated tubes. Quantum effects are included through implementation of the path integral formalism. Comparison with classical simulations gives an indication of the importance of quantum effects for hydrogen adsorption. Quantum effects are important even at 298 K for adsorption in tube interstices. We compare our simulations with experimental data for SWNTs, graphitic nanofibers, and activated carbon. Adsorption isotherms from simulations are in reasonable agreement with experimental data for activated carbon, but do not confirm the large uptake reported for SWNTs and nanofibers. Although the adsorption potential for hydrogen in SWNTs is enhanced relative to slit pores of the same size, our calculations show that the storage capacity of an array of tubes is less than that for idealized slit pore geometries, except at very low pressures. Ambient temperature isotherms indicate that an array of nanotubes is not a suitable sorbent material for achieving DOE targets for vehicular hydrogen storage.