We present systematic molecular dynamics simulation studies of hydrogen storage in single walled carbon nanotubes of various diameters and chiralities using a recently developed curvature-dependent force field. Our main objective is to address the following fundamental issues: 1. For a given H2 loading and nanotube type, what is the H2 distribution in the nanotube bundle? 2. For a given nanotube type, what is the maximal loading (H2 coverage)? 3. What is the diameter range and chirality for which H2 adsorption is most energetically favorable? Our simulation results suggest strong dependence of H2 adsorption energies on the nanotube diameter but less dependence on the chirality. Substantial lattice expansion upon H2 adsorption was found. The average adsorption energy increases with the lowering of nanotube diameter (higher curvature) and decreases with higher H2 loading. The calculated H2 vibrational power spectra and radial distribution functions indicate a strong attractive interaction between H2 and nanotube walls. The calculated diffusion coefficients are much higher than what has been reported for H2 in microporous materials such as zeolites, indicating that diffusivity does not present a problem for hydrogen storage in carbon nanotubes.