We apply a statistical mechanical theory on clathrate hydrates to an exploration of the phase behaviors of hydrocarbon and noble gas clathrate hydrates. Two- and three-phase coexisting conditions in the whole space of thermodynamic variables (temperature, pressure, and composition) are evaluated only from intermolecular interactions for water and guest species. The occupancy of guest molecules in various types of cages is also calculated. We find that a small difference in the guest size gives rise to a rich variety of phase behaviors, notably for the shape of the two-phase boundary and the occupancy. Ethane clathrate hydrate is found to exhibit the most drastic and intriguing features in various properties arising from its non-stoichiometry. We investigate the phase behaviors of clathrate hydrate in terms of the partial molar quantities derived from the chemical potentials of guest and water. Our method also allows exploring the aqueous solution of an apolar guest molecule in the low temperature and high pressure regime coexisting with the corresponding clathrate hydrate for which the free guest fluid phase is substituted at high temperatures. It is shown that the temperature dependence of methane solubility in liquid water in the presence of clathrate hydrate is opposite to that being in equilibrium with the methane fluid without clathrate hydrate. This phenomenon is elucidated by a substantial decrease in the chemical potential of methane from the hydrate/guest boundary to the hydrate/water.