Rare gas adsorption was studied on suspended individual single walled carbon nanotubes and graphene. The devices were fabricated as field effect transistors. Adsorption on graphene was studied through two-terminal conductance. On nanotube devices adsorption was studied through conductance while the coverage (density) of the adsorbates was determined from the mechanical resonance frequency shifts. The adsorbed atoms modified the conductance of the nanotube field effect transistors, in part through charge transfer from the adsorbates to the nanotube. By tracking the shifts of conductance as a function of gate voltage, G=G(Vg), and comparing these shifts with the periodicity of the Coulomb blockade oscillations we quantified the charge transfer to the nanotubes with high accuracy. For all studied gases (He, Ar, Kr, Xe, N2, CO, and O2) the charge transfer had a similar magnitude and was rather small, on the order of 10^-5 to 10^-3 electrons per adsorbed atom. The nanotube devices displayed two classes of adsorption behavior. On some devices the monolayers exhibited first-order phase transitions analogous to those that occur in adsorbed monolayers on graphite. On other devices phase transitions within the adsorbed monolayers were absent. We present evidence that a highly uniform layer of contaminants deposits on the surface of suspended nanotube devices either upon cooldown in the cryostat or at room temperature from air. These contaminants modify the adsorption behavior preventing the adsorbed monolayers from exhibiting the first order phase transitions expected to occur on a clean surface. A similar type of contamination leading to virtually identical effects occurs on suspended graphene. In the low coverage regions of isotherms on nanotubes we observe Henry's law behavior, demonstrating a high uniformity of the surface and allowing us to accurately determine the single particle binding energy to this surface. The determined binding energies were 776+-10 K for Ar, and 997+-37 K for Kr. In the second part of the dissertation we present the first measurements of adsorption on a pristine graphene surface, exposed through aggressive electric current annealing. On graphene the rare gas adsorbates form monolayers with phases analogous to those on graphite, but with phase transitions occurring at slightly higher pressures due to a reduction of binding energy. The condensations of monolayers with phases not commensurate with the graphene lattice resulted in a slight shift of the charge neutrality point of monolayer graphene corresponding to a change of carrier concentration on the order of 10^9 e/cm^2. Adsorption of N2 and CO, which formed a Root 3 X Root 3 commensurate solid monolayer, produced a dramatic reduction of the two-terminal conductance of graphene by as much as a factor of three. This effect is possibly connected with the opening of a band gap expected to occur in such structures. We observe hysteretic behavior in the adsorbed Root 3 X Root 3 commensurate monolayers on freestanding graphene, which is likely due to the interaction of two adsorbed monolayers on opposite surfaces of the graphene sheet.