Nervous system evolved only once, about 3 billion years after life started, and nothing analogous to it ever evolved in any other lineage. [Urbilaterian]

From Science, July 3 2009, p. 24-26, "On the origin of the nervous system":

Assembling these components into a cell a modern neuroscientist would recognize as a neuron probably happened very early in animal evolution, more than 600 million years ago... Scientists also disagree on which animals were the first to have a centralized nervous system and how many times neurons and nervous sytems evolved independently ... [Leonid Moroz:] "Neurons may have appeared in multiple lineages in a relatively short time."

p. 26:

If the bilaterian ancestor had a diffuse nervous system, centralized nervous systems must have originated multiple times in multiple bilaterian lineages... On the other hand, if the ancestor had a centralized nervous system, several lineages... must have later reverted to a diffuse nervous system. ... Most researchers now agree that equally complex - but anatomically different - brains have evolved in birds, mammals, and other animal lineages, Northcutt says: "At least four or five times independently, ... major radiations of vertebrates have evolved complex brain structure."