Possibly the single biggest cause of cats not using the litter box is a medical condition called Feline Urinary Tract Infection (UTI). Your cat often may not display outward symptoms of discomfort and pain early on. It's only after your kitty feels significant pain, time and time again, that she stops using her litter box because she associates her urinary pain with the cat litter box.
However, there are a few signs you should be on the lookout for. While none of us really want to watch our kitty use the litter box, it's a good idea to observe her a couple times a week. This way, you can separate normal litter box behavior and habits from those that indicate something is not quite right.
First, we are looking to see if our cat cries or howls in obvious pain while she's urinating. If this is the case, run, don't walk to the phone, and call your vet immediately!
Next, even if kitty does her business in silence, look at the urine ball (or puddle) before she buries it. If you see any tinge of red or pink - get your cat to the vet as fast as you can, because she definitely has a UTI in full bloom.
After she uses the box and covers her business, if she licks her genitals
excessively, and meows, you can be pretty sure she has a feline UTI. Particularly if you see this behavior coupled with "accidents" around the house, you can be pretty certain you are dealing with a UTI.
A few minutes now can save both you and your cat discomfort later. By knowing what is normal for her, you will be able to catch any problems early and get the UTI cleared up before it becomes too uncomfortable.