Hinton's DropOut [1] and Wan's DropConnect [2] have ameliorated some of the overfitting issues present in traditional NN's. In fact, DropConnect in conjunction with deep learning are responsible for new records being set on classical datasets such as MNIST.
[1] http://arxiv.org/pdf/1207.0580.pdf [2] http://cs.nyu.edu/~wanli/dropc/