As with neural networks, it is good for producing solutions to problems where a large amount of information is presented and there are few "logical" directions as to how to process it. An example here would be steering a robot through a maze: programmer Craig Reynolds has managed to evolve a "critter" that can run through a predefined maze. Critters were allowed a limited sort of vision, and various functions to allow them to "steer" around the maze.
The measure of fitness here was the number of "steps" the critter managed to take before colliding
with any obstacles (which was "fatal", in this case). After several iterations through the genetic system, he was
able to evolve critters that would be able to navigate his maze well, although all his iterations were conducted with
the same maze, starting position and orientation, so his critters were unsuited to navigating any other mazes.