As others have pointed out, we have an intrinsic circadian cycle that runs just slightly longer than 24 hours. Other organisms, such as mice, can have slightly shorter cycles at around 23.5 hrs. Hence the term circadian: from Latin circa, meaning "about" and dies, meaning "day".

This circadian rhythm is built-in and governs multiple functions, of which sleep is one. Temperature and cortisol secretion, for example, also oscillate with a similar daily period. We know this from some crazy time-isolation experiments where subjects lived in caves or isolated rooms with no indicators of time. Because our natural cycle is longer than 24 hours, these subjects slept a little bit later everyday and after some time they ended up drifting their sleep onset so that it occured during our daytime (they had no idea whether it's day or night). Later, it was discovered that exposure to light can reset this cycle so that it prevents this natural daily advance in sleep onset. This is why we follow a 24 hour cycle in the outside world where sunlight resets this cycle so that it begins at a new phase ever day.

Importantly, the maximum amount of time that this cycle can be reset is 3 hours per day. This is why it takes a few days for jet lag to really clear up.

On other planets, we would still follow our 25 hr circadian cycle but we'd reset it everyday depending on availability of light. If the day on that other planet was something be like 36 hours, my guess is that we'd be constantly jetlagged if we planned our activities around our circadian cycle.

On a related note, these time-isolation experiments found that the subjects began to do something weird after about a month where they would stay up way past their bedtime and then sleep for 15 hours without even realizing it. They then bounced back to a normal 25 hour cycle before getting desynchronized again and starting a crazy cycle 40 to 50 hours long. The researchers figured out that this was linked to body temperature at time of sleep onset. Basically, long sleeps always began at high body temperature and normal sleeps at low body temperature.