The long-term mean properties of the global climate system and those of turbulent fluid systems are reviewed from a thermodynamic viewpoint. Two general expressions are derived for a rate of entropy production due to thermal and viscous dissipation (turbulent dissipation) in a fluid system. It is shown with these expressions that maximum entropy production in the Earth's climate system suggested by Paltridge, as well as maximum transport properties of heat or momentum in a turbulent system suggested by Malkus and Busse, correspond to a state in which the rate of entropy production due to the turbulent dissipation is at a maximum. Entropy production due to absorption of solar radiation in the climate system is found to be irrelevant to the maximized properties associated with turbulence. The hypothesis of maximum entropy production also seems to be applicable to the planetary atmospheres of Mars and Titan and perhaps to mantle convection. Lorenz's conjecture on maximum generation of available potential energy is shown to be akin to this hypothesis with a few minor approximations. A possible mechanism by which turbulent fluid systems adjust themselves to the states of maximum entropy production is presented as a self-feedback mechanism for the generation of available potential energy. These results tend to support the hypothesis of maximum entropy production that underlies a wide variety of nonlinear fluid systems, including our planet as well as other planets and stars.