Adsorbed natural gas (ANG) storage systems are based on nanoporous adsorbents with a tailored porous structure. Activated carbons are among the most promising and widely used candidates for this application, which is explained by the availability and abundance of raw material resources. In the present work, several series of activated carbons prepared from various precursors (coconut shell, peat, polymers, silicon carbide, and mineral coal) by different routes of physical and thermochemical activation were considered in the context of the adsorbed natural gas storage applications. Based on the Dubinin theory of volume filling of micropores and BET method, the porous structure of these adsorbents was evaluated from standard adsorption isotherms. The XRD, SAXS, and SEM measurements revealed variations in the textural and morphological properties of the adsorbents and their dependence on the precursor and synthesis procedure. The pore sizes evaluated from the adsorption and SAXS data were compared. Experimental data on methane adsorption at the temperature of 303 K and pressures of 0.1, 3.5, and 10 MPa made it possible to identify the most effective adsorbents. It was shown that the adsorption properties of ACs prepared from peat and mineral coal are determined by surface chemistry inherited from the precursor and activating agent. In contrast, the adsorption performance of ACs from polymer and coconut shell depends solely on the pore volume and pore dimensions. The adsorption effectiveness of each AC varies with pressure as a function of textural properties. Thus, a selection of an optimal adsorbent should be adjusted for thermodynamical coditions of ANG system.