Your cat may be ill. According to the Cornell University Feline Health Center, a cat that stops using its box may be suffering from FUS, a range of disorders of the lower urinary tract. A cat with FUS is extremely uncomfortable and spends a lot of time straining to urinate, in or out of the litter box. Another medical reason a cat may avoid the litter box is blocked anal glands. The first step to take when a cat suddenly exhibits a change in litter box habits is to have a veterinarian rule out any physical problems.
Un-neutered cats, both male and female, tend to spray urine indiscriminately.
A cat that's disturbed when using the litter box may tend to soil elsewhere. Try placing the box in a secluded private area.
If the home has more than one cat, one may be ambushing the other when it uses the litter box.
For many cats a significant change in the household, a new baby, spouse, pet, etc., may influence litter box problems. Use a lot of TLC to alleviate the problem.
Other than a physical problem, the single most important reason why cats don't use their litter box is because of the litter itself. Many cats have a definite preference for a certain type of litter so experiment and always keep in mind a clean litter box is essential.
When cleaning up accidents, many owners will use an ammonia or ammonia based cleaner. This will only attract the cat back to the same spot.
Try confining the cat in a small area with food at one end and the litter box at the other. This will force the cat to use the box as she won't soil near her food. Start feeding the cat in the areas she has soiled.
Senior cats may develop litter box problems. Add another litter box if possible to cut down on travel time to the box. Switch to a box with lower sides.
A small drop of ammonia in the bottom of a litter box may encourage a cat to use the box. Conversely, too much may convince the cat that the box is dirty.