Lightbulb is a c++ artificial neural network framework, which is easy to use and powerful. It was especially written for to be used in games, but theoretically it can be used everywhere. The code is opensource and can be found on github.
In this example LightBulb was used to generate an AI which can play TicTacToe perfectly (perfectly means that it never looses!). The used neural network has four layers, with 18, 10, 10 ,9 neurons and uses shortcut edges. The special thing about this example is that the neural network was trained by coevolution. So only by playing network against another network from the population and determining which one is better, a perfect AI has been found.
See the documentation.