Cats are notoriously picky. That very quality often contributes to what is known as inappropriate elimination. The most common form of inappropriate elimination is inappropriate urination. There are factors outside of a cat's pickyness that can cause this bane of cat owners everywhere (or is that cat staffers?), including medical problems.
Some cats will stop using the litter box for a very basic reason: they don't like it. Among the reasons for this include the litter box being dirty, a general dislike for the litter of the owner's choice, a change in litter, movement of the litter box, and other cats using the litter box. Cats are meticulously clean, and, like most humans, prefer their bathrooms to be as such as well. A litter box we humans consider fine can be positively repulsive to a cat's delicate nose. Cats will also not use the litter box because they don't like the litter. This can happen from day one of using the litter or randomly start. Usually it has to do with the texture of the litter, of which there are many. Clay, scoopable, crystals, pine shavings...if it can even maybe absorb, it has somehow been made into cat litter. Those pads on the bottoms of cat paws are sensitive, and the wrong texture can cause a cat to decide to eliminate elsewhere. If this aversion begins randomly, one should definitely check into a medical cause behind it. Painful paws or a urinary tract infection, among other things, can cause Kitty to change his tune about a previously used litter. A change in litter can cause aversion to using the litter box in much the same way. After all, if Kitty doesn't like it, Kitty won't use it.
Cats have even been known to eliminate outside the litter box because it moved. This can be because the cat is confused or stressed- cats like things to be one way and stay that way- or because he doesn't like the new location. Some cats do not react well to having their bathroom in a high-traffic area or in spaces with lots of noise, such as a laundry room or by the dishwasher. Those things can cause a cat to find elsewhere to go to the bathroom. And finally, other cats. It is suggested that a cat owner have one litter box for each cat they have, plus one. This is because some cats do not like to go where other's have gone. And if someone else has had first-dibs on the only litter box, the feline may make a litter box of his own. Such as on your sofa, clean laundry, or in that incredibly-inaccessible-unless-you're-a-cat space behind the fridge. If it's close to the litter box, however, there's a chance your cat may just have horrible aim.
Then there's the more serious causes of inappropriate elimination: medical causes. These can range from stress to UTIs to other more serious ailments. Stress can cause cats to eliminate, especially urinate, in areas other than the litter box to mark his territory. Comforting for the cat, a complete pain for the humans who have to live with the animal. Cat urine has a very strong odor, and it is most unpleasant and difficult to remove. Feline pheromone sprays or diffusers, or even Kitty Prozac, can usually relieve stress and get a household smelling normal again. Urinary tract infections (UTIs) can cause pain when a cat uses the litter box, just like UTIs in humans can cause it to burn when urinating. Cats don't know that there's something wrong and begin to associate the pain with the litter box, leading to them going somewhere else. With cats, it doesn't always have to make sense. UTIs are usually resolved with an antibiotic, lots of water, and a special diet.
So there are many reasons why a cat may answer nature's call outside the litter box. The best thing to do is take the cat to the vet if the problem doesn't resolve itself in a few days (and hopefully with the owner's sanity intact) , just to make sure that there's not a medical reason behind the inappropriate elimination. If no medical cause is found, a vet can help the owner decide what to do to try and alleviate the problem.