SIMBRAIN is a free tool for building, running, and analyzing neural-networks (computer simulations of brain circuitry). Simbrain aims to be as visual and easy-to-use as possible.
Fast Artificial Neural Network Library is a free open source neural network library, which implements multilayer artificial neural networks in C with support for both fully connected and sparsely connected networks. Cross-platform execution
J. Thangavelautham, and G. D'Eleuterio. PPSN VIII: Proc. 8th Int'l Conf. on Parallel
Problem Solving from Nature, volume 3242 of LNCS, page 991--1000. Birmingham, UK, Springer, (18-22 Sept. 2004)