Earth's obliquity would vary chaotically from 0° to 85° were it not for the presence of the Moon (J. Laskar, F. Joutel, and P. Robutel, 1993,Nature361,615-617). The Moon itself is thought to be an accident of accretion, formed by a glancing blow from a Mars-sized planetesimal. Hence, planets with similar moons and stable obliquities may be extremely rare. This has lead Laskar and colleagues to suggest that the number of Earth-like planets with high obliquities and temperate, life-supporting climates may be small.To test this proposition, we have used an energy-balance climate model to simulate Earth's climate at obliquities up to 90°. We show that Earth's climate would become regionally severe in such circumstances, with large seasonal cycles and accompanying temperature extremes on middle- and high-latitude continents which might be damaging to many forms of life. The response of other, hypothetical, Earth-like planets to large obliquity fluctuations depends on their land-sea distribution and on their position within the habitable zone (HZ) around their star. Planets with several modest-sized continents or equatorial supercontinents are more climatically stable than those with polar supercontinents. Planets farther out in the HZ are less affected by high obliquities because their atmospheres should accumulate CO2in response to the carbonate-silicate cycle. Dense, CO2-rich atmospheres transport heat very effectively and therefore limit the magnitude of both seasonal cycles and latitudinal temperature gradients. We conclude that a significant fraction of extrasolar Earth-like planets may still be habitable, even if they are subject to large obliquity fluctuations.