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
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.
If you are starting with Neural Networks you should check out my online book on the subject. It contains over 300 pages of information on Neural Network Programming in Java. You can access it here.