Thinking outside the box is one thing but when your cat starts going outside the box it can cause serious issues (not to mention damage) in your household. One of the most important senses in a cat is olifactory (smell) and they use it the most in urine and feces marking. There are several reasons why cats suddenly start this behavior, some of them are:
Marking Territory - if cats feel their territory is threatened, maybe by a new cat or the presense of a Tom outside, they will often deposit urine and feces at the perimeter (along a wall) of the home to "claim" it.
Hormones - unaltered cats mark the most, which is hormone driven. However, both spayed and neutered cats will also spray urine, just less frequently.
Smells - unidentified smells may lead a cat to reaffirm their territory with urine and/or feces marking
Changes - cats are very routine-oriented and do not like changes. If you see sudden behavior changes take note of what has changed in their environment (cleaning products, new air fresheners, litter, diet, etc.)
Dirty - because smell is so important to cats, they won't use a dirty litter box; it's important to keep it very clean. However, with kittens, it's important to teach them where it's appropriate to go so be sure to leave a bit of feces in the box so they can orient on it.