Below are the links to web pages with mini-neurosimulators that allow you to experiment with various neural network paradigms, such as Willshaw Networks, Hopfield Networks, Perceptron, Backprogation, Kohonen Maps, and more. If you don't know what these are you can still give it go! Or first read up on neural networks.
User guide mini-neurosimulators
Modular Neural Networks: Kohonen Maps
Perceptron and Backprogatation