Not only is it possible for a cat to survive a fall of 14 stories (or more), a cat is more likely to survive such a fall than one from only four stories (at least according to my freshman physics textbook; like everything else I learned during my freshman year, I trust it to be 100% correct). The reasoning is thus:

A cat has little ability to sense its absolute speed (which makes sense, since any good relativist will tell you that there's no such thing as an "absolute speed"). What a cat does have is a sense of proprioception, which tells the cat how fast it's accelerating. When a cat falls out of a window it begins accelerating at something close to 9.8 m/s; this really freaks the cat out, so it assumes its "I'm in danger" posture. Specifically, it tucks its head in, pulls its feet under its body, and curves its spine. This is a good thing for the cat to do if something has just thrown it; the important parts are towards the inside where they are less likely to get injured upon impact. Unfortunately, it also makes the cat much more aerodynamic.

Curled up like this, a cat cuts through the air suffering very little drag. The low surface area of this shape means the cat has a high terminal velocity (maybe 15m/s?). If it strikes the ground going this fast, it is unlikely to survive (at least not without serious injury).

Luckily, after the cat has fallen seven or eight stories, it begins to closely approach its terminal velocity. This means that the drag due to air resistance is equal to the force of gravity, so the cat is no longer accelerating. This allows the cat to calm down enough to more thoroughly appraise the situation. Cats apparently all have an instinctive understanding of certain laws of physics, or at least they know they're more likely to survive a fall it they spread themselves out. They stretch their legs and neck out, increasing their surface area, which decreases their terminal velocity. This slows the cat down considerably (and makes it look kinda like a flying squirrel). At this slower speed it can easily survive the fall (theoretically from any height, though 32 stories is the highest on record).

Or so I've been told. I may have been lied too.