Some recent work in Neuron (full article; easy to read summary) shows how hippocampal neurons can cause neural progenitor cells to produce new neurons in the hippocampus. I find this fascinating since the network literally is replacing itself through its own dynamics.
The mechanism seems to be that GABAergic cells synapse onto progenitor cells and cause calcium entry due to the depolarization. (GABAergic synapses are often excitatory in young cells which have elevated intracellular chloride levels.) The increased calcium entry leads then to activation of genes coding for neuronal differentiation-related proteins.
Also, here’s some earlier work from Malenka’s lab along the same lines.