Unlike some animals, cats need to be fed regularly. In fact, if a cat does not eat for 24h, it can result in permanent liver damage.
If you are planning on going on a vacation, and leaving your cat alone at home, make sure you have someone stop by once per day to feed your cat.
Although cats can survive for a couple days without food, it is very unhealthy, and too much time after that, your cat can die.
If you already left your house, and forgot to find someone to feed your cat for you while you are away, you should call your friends and family in the area and ask them to do it for you asap.
If you are planning on going on vacation, and there is no one that is available to feed your cat for you, you can take your cat to a animal day care, where they will take care of your cat until you return.
Animal day cares can be fairly costly, so it is best to find a friend to feed your cat while you are away.
Some people might say that cats can go a long time without eating. Although cats can technically survive, it causes major health issues, and even no food for two days can result in a very sick cat.
For example, these cats were saved from a house where they went weeks without eating. (After their owner died)
Although they survived, they were in extremely poor health, and needed medical help right away.