No video game can be truly organic, at least not with the current technology. Everything that happens is governed by programming; even seemingly "random" events are just a series of scripts reacting to one another.
Still, the illusion of randomness and free will is one of the most compelling aspects of games. An excellent example can be found in Skyrim. Just the other day, I stepped out of a gloomy dungeon to a winding, rocky path beside a stream. A light snow had just started to fall, and I was ready to hit the road again towards my objective (some fort at the western edge, the details didn't concern me).
A dragon swoops in from the horizon. I was surprised, but after a few dragon encounters, I shouldn't have been. This was routine; dragon battles aren't scheduled, but they are predictable. But it was the manner of its arrival that surprised me the most. Just before attacking me, the dragon changed course to immolate a a gang of highwaymen further down the road.