A three-dimensional general-circulation climate model is used to simulate climates of Earth-like planets with extreme axial tilts (i.e. ‘obliquities’). While no terrestrial-planet analogue exists in the solar system, planets with steeply inclined spin axes may be common around nearby stars. Here we report the results of 12 numerical experiments with Earth-like planets having different obliquities (from 0° to 85°), continental geographies, and levels of the important greenhouse gas, CO2. Our simulations show intense seasonality in surface temperatures for obliquities [ges ]54°, with temperatures reaching 80–100 °C over the largest middle- and high-latitude continents around the summer solstice. Net annual warming at high latitudes is countered by reduced insolation and colder temperatures in the tropics, which maintains the global annual mean temperature of our planets to within a few degrees of 14 °C. Under reduced insolation, seasonal snow covers some land areas near the equator; however no significant net annual accumulation of snow or ice occurs in any of our runs with obliquity exceeding the present value, in contrast to some previous studies. None of our simulated planets were warm enough to develop a runaway greenhouse or cold enough to freeze over completely; therefore, most real Earth-like planets should be hospitable to life at high obliquity.