When should I use genetic algorithms as opposed to neural networks?

From wikipedia:

A genetic algorithm (GA) is a search technique used in computing to find exact or approximate solutions to optimization and search problems.

and:

Neural networks are non-linear statistical data modeling tools. They can be used to model complex relationships between inputs and outputs or to find patterns in data.

If you have a problem where you can quantify the worth of a solution, a genetic algorithm can perform a directed search of the solution space. (E.g. find the shortest route between two points)

When you have a number of items in different classes, a neural network can "learn" to classify items it has not "seen" before. (E.g. face recognition, voice recognition)

Execution times must also be considered. A genetic algorithm takes a long time to find an acceptable solution. A neural network takes a long time to "learn", but then it can almost instantly classify new inputs.

A genetic algorithm (despite its sexy name) is, for most purposes, an optimization technique. It primarily boils down to you having a number of variables and wanting to find the best combination of values for these variables. It just borrows techniques from natural evolution to get there.

Neural networks are useful for recognizing patterns. They follow a simplistic model of the brain, and by changing a number of weights between them, attempt to predict outputs based on inputs.

They are two fundamentally different entities, but sometimes the problems they are capable of solving overlap.