The number of layers is one of the factors controlling model complexity.
Interesting, the number of units in the hidden layers isn't as important as the size of the weights of the hidden units. This is a famous result from the 1990's.
Hence, a principled way of controlling overfitting in NNs is: Pick a large enough number of weights that you don't underfit, and apply l2-regularization to the hidden unit weights. This is superior to fiddling with the number of hidden units in an unregularized net.
A related result is that you can control model complexity by imposing sparsity on the activations of the hidden units.