If your cat isn't using the litter box, though, it's important to ask yourself why. Usually the cat has a reason for its behavior, and it's up to you to figure it out.
One of the biggest reasons why cats stop using the litter box properly is because of urinary tract infections. If your cat is peeing in various places around the house, and every time it's a different place, chances are she has a UTI. Not every cat behaves this way, though, so testing for a UTI should always be one of the first things you do if your cat develops a problem with using her cat box -- especially if this is uncharacteristic for her.
Another major cause for cat box problems is simple lack of cleanliness. Cats are finicky creatures, so if you let the cat boxes get too dirty on a regular basis, they will take their business elsewhere, so to speak. Cats have an instinct to go in a clean place every time, so it's a tribute to their willingness to please that they do their business in cat boxes at all, really. Females are especially finicking, by the way, and are more likely to pee outside the box once it gets dirty.
And finally, don't underestimate a cat's willingness to pee outside the box just to piss you off (please excuse the pun). I've had two cats who, at different times, very definitely peed on something to let me know they were unhappy with me. One had just gotten in trouble for something wholly unrelated, and the other was acting out because I was away from home too often.
Unfortunately, once a cat starts going outside the box, it can be hard to resolve the problem. Keeping the litter boxes extra clean, thoroughly cleaning the site of any accidents, and trying to identify what's bothering the cat (dog not letting her get to the litter box easily enough, for example?) are of paramount importance, and of course don't forget to check for a UTI too!