In a recent letter [T. Yildirim and S. Çiraci, Phys. Rev. Lett. 94, 175501 (2005)], the unusual hydrogen storage capacity of Ti decorated carbon nanotubes has been revealed. The present paper extends this study further to investigate the hydrogen uptake by light transition-metal atoms decorating various carbon-based nanostructures in different types of geometry and dimensionality, such as carbon linear chain, graphene, and nanotubes. Using first-principles plane-wave method we show that not only outer but also inner surface of a large carbon nanotube can be utilized to bind more transition-metal atoms and hence to increase the storage capacity. We also found that scandium and vanadium atoms adsorbed on a carbon nanotube can bind up to five hydrogen molecules. Similarly, light transition-metal atoms can be adsorbed on both sides of graphene and each adsorbate can hold up to four hydrogen molecules yielding again a high-storage capacity. Interestingly, our results suggest that graphene can be considered as a potential high-capacity H2 storage medium. We also performed transition state analysis on the possible dimerization of Ti atoms adsorbed on the graphene and single-wall carbon nanotube.