Reason #1: Busy Location
Cats are private animals. While a dog will do its business outside with everyone in the world watching and think nothing of it, cats have to relax in order to get the job done. If the box is located in an area where people are always coming and going, that's going to be upsetting to your cat and he or she is likely to go elsewhere in the house, usually some place quiet like a corner.
Now, if you haven't moved the litter box and if the traffic in the area hasn't increased lately, but your cat has suddenly stopped using it, there's probably another good reason.
Reason #2: Cat Preferences
Cats seem to be a lot pickier than dogs about everything from toys to food to sleeping locations. They are also sometimes very picky about their litter boxes. Many cats like certain types of litter better than others, possibly because of the way it feels on their paws. Other cats have litter box type preferences. While some love to have the covered boxes for more privacy, others prefer something that is a little more open so they can what is going on around them.
As with the first reason, if you haven't made any changes that might upset your cat's preference but he or she has suddenly stopped using the litter box, there is probably a different reason as the root cause.
Reason #3: Medical Problems
In some cases, a urinary infection or some other health problem can cause cats to have litter box problems. They may have a hard time going to the bathroom or may associate the litter box itself with discomfort which makes the box undesirable. If the sanitary reasons and the first two reasons don't seem to explain the sudden change in your cat's behavior, you should seek advice from a veterinarian immediately. Your cat might have a very serious health problem.
If you cat is defecating outside the litter box, he or she may have worms, gas, or other intestinal distress so a vet visit is definitely recommended. Remember that once your cat starts using the bathroom outside of the litter box, cleaning it with a solution that will destroy the enzymes in the urine or feces is essential. Otherwise your cat is going to continue to view that spot as an appropriate choice for going to the bathroom.
Reason #4: Behavioral Problems
If you've ruled out all of the other reasons, you'll have to start thinking like your cat and trying to pinpoint what may be the real problem. Anxiety can be one reason. A cat that doesn't like to be left alone may use the bathroom outside the litter box as a sign of separation anxiety. A cat that's angry because a new family member or pet has come into the picture may also start protesting by not using the litter box correctly.
When emotional issues are involved, you may find it harder to pinpoint the cause. However, you may be able to work with your vet on figuring out the best way to solve the problem so your cat can start using the litter box again and you can cut down on cleaning the carpet and other areas of your home.
Unfortunately, it's very hard to fix a behavioral problem if you don't know the exact cause. However, with patience and love, you might be able to find the cause and fix the problem. Sometimes medication can help. Do your research before taking any drastic measures. Always remember that no matter what he or she does, it's not done to spite you. Cats are not capable of those 'humanoid' feelings. If your cat is having litter box problems, he doesn't deserve to be punished or God forbid, euthanized, just because we don't understand his reasons.