Although cats should always have clean drinking water available, a house cat can survive for a few days or sometimes up to a week without water. House cats were originally from desert climates, so they are predisposed to going without water for longer than most other household pets.
If a cat is eating moist food, it likely gets the majority of its hydration needs met through the water in the food. Similarly, feral cats acquire water largely from prey. This is why cats can often survive for long periods of time in the wild without drinking water.