Abstract Conventionally, a habitable planet is one that can support liquid water on its surface. Habitability depends on temperature, which is set by insolation and the greenhouse effect, due mainly to CO2 and water vapor. The CO2 level is increased by volcanic outgassing and decreased by continental and seafloor weathering. Here, I examine the climate evolution of Earth-like planets using a globally averaged climate model that includes both weathering types. Climate is sensitive to the relative contributions of continental and seafloor weathering, even when the total weathering rate is fixed. Climate also depends strongly on the dependence of seafloor weathering on CO2 partial pressure. Both these factors are uncertain. Earth-like planets have two equilibrium climate states: (i) an ice-free state where outgassing is balanced by both weathering types, and (ii) an ice-covered state where outgassing is balanced by seafloor weathering alone. The second of these has not been explored in detail before. For some planets, neither state exists, and the climate cycles between ice-covered and ice-free states. For some other planets, both equilibria exist, and the climate depends on the initial conditions. Insolation increases over time due to stellar evolution, so a planet usually encounters the ice-covered equilibrium first. Such a planet will remain ice covered, even if the ice-free state appears subsequently, unless the climate receives a large perturbation. The ice-covered equilibrium state covers a large fraction of phase space for Earth-like planets. Many planets conventionally assigned to a star’s habitable zone may be rendered uninhabitable as a result.