This was just a random thought that crossed my mind, and I'm sure there is a simple physics explanation. Say we have a leaky faucet 20 feet above the ground that lets out the exact same amount of water every few seconds or so. Why is it that the splash pattern for every drop is never the same as any other drop? Now it's not like I've sat there and observed every splash, but sometimes its obvious, like a certain splash's water reached a farther distance than another splash. If we are letting the same amount of water come out everytime, and nothing else changes, why do the splashes vary? (pretend the water disappears off the ground after every splash, that way every splash has the same environment.)
In order for the splashes to actually be the same, each drop would have to be exactly identical, down to the exact positions and velocities of each molecule in the drop. It's basically impossible that two drops would ever be the same to that level of detail.
The fact that this is a chaotic system, as Georg said, means that even tiny differences in the state of each drop can have a significant effect on the splash pattern.
By the way, the same would have to apply to the environment: it would have to be identical, down to the molecular structure of the floor, for every drop. That would never happen in real life.