I have a good cat/balcony story - amazing, but true. I was there to see it.
My college roomie had three kitties while she and her husband were living on the 12th floor of an apartment building. They weren't supposed to be on the balcony but they were always scratching at the screen and trying to get out there.
One day she called me in hysterics because she couldn't find the youngest, a little black cat named Twizzler. She hadn't left the apartment all day but there was a small hole in the screen door. She was terrified that the cat had fallen.
Her husband came home from work and we all searched. It only took a few minutes for her husband to find Twizzler, terrified and hiding under a bush, on the ground almost directly beneath their balcony. We are quite sure that she fell from their balcony, but to this day we have no idea how she survived.
Twizzler was, of course, rushed to the vet, and other than a few broken ribs, suffered very little physical damage. She was, however, never quite the same open, affectionate, curious cat she had once been - she's now very cautious and anxious. It's been five years, and they live in a house now, but for the duration of their lease you better believe the balcony door stayed shut and latched.