Conway's game of Life is very famous - old (it was first modelled by hand with black and white counters), it's one of my standard exercises when picking up a new language. Simple rules display complex emergent behaviour.

Barnsley's Fern is something I've just stumbled across - a fractal, where a simple set of four equations can generate stunningly life-like ferns. Barnsely speculates that the growth of a fern must be related ... 

 Four examples of a fern produced by the same four equations with slightly different parameters.

While at university I met Craig Reynolds who was working on his Boids simulation, where a set of "entities" given very simple rules (stay close to the others, but not to close) give rise to complex, life-like flocking behaviour.