There was an MSDN Magazine article about .NET and Neural Networks, "Give Your .NET App Brains and Brawn with the Intelligence of Neural Networks" and I'm sure there are many more articles of the given topics on the net. Just search at MSN Search or try to visit some big .NET tutorial sites (for example CodeProject)
Library with API (source code included): http://franck.fleurey.free.fr/NeuralNetwork/
Article covering the basics of back propagation learning (source code included): http://www.c-sharpcorner.com/Code/2004/Jan/NeuralNetSim.asp
Neural network OCR: http://www.codeproject.com/csharp/Neural_Network_OCR.asp
Neural network class: http://www.csharphelp.com/archives2/archive407.html
Links to resources with general info on neural nets, genetic algorithms, etc: http://www.makhfi.com/resources.htm
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p.s.- it actually says something!
You can found a C# Source in www.codeproject.com
Simple Fuzzy Logic Library for .Net: http://sourceforge.net/projects/fuzzynet