Note: this answer was correct at the time it was made, but has since become outdated.
It is rare to have more than two hidden layers in a neural network. The number of layers will usually not be a parameter of your network you will worry much about.
Although multi-layer neural networks with many layers can represent
deep circuits, training deep networks has always been seen as somewhat
of a challenge. Until very recently, empirical studies often found
that deep networks generally performed no better, and often worse,
than neural networks with one or two hidden layers.
Bengio, Y. & LeCun, Y., 2007. Scaling learning algorithms towards AI. Large-Scale Kernel Machines, (1), pp.1-41.
The cited paper is a good reference for learning about the effect of network depth, recent progress in teaching deep networks, and deep learning in general.