NearNeural is a neural net library written in purest Java. It's logically very clean, retaining the component based distinctions made in the theory (nodes, edges etc. are all objects). Though it has been optimised through the use of some caching methods, and is easily fast enough for simple tasks, it is best suited to educational or experimental use.
The architecture also allows it to be very flexible, and it's capable of emulating many kinds of net (though it was originally designed as a feed-forward backprop system). I've used it to perform OCR, classify texts by language, produce estimates of various other algorithms' output and solve the travelling salesman problem.
Download NearNeural-0.3.tar.gz.
NearNeural should be considered a general purpose (or educational) library, and comes fully JavaDoc annotated, as well as being bundled with a few simple examples. It also contains code to display a net using Java's Swing or AWT systems.
I've uploaded the documentation here, so you can browse it without having to regenerate it.