Comparison with other free neural network packages:

Genesis, Neuron
Genesis and Neuron are geared towards modeling biophysically realistic neurons. The emphasis is on analysis of single neurons or small groups of neurons.

SNNAP
SNNAP is intermediate between Genesis and Neuron on the one hand and Simbrain on the other, providing tools for simulating spiking neurons using "mathematical descriptions of ion currents and intracellular second messengers and ions." Simbrain does have some spiking neurons but they are early in development.

BrainWave
BrainWave is similar to simbrain, though its interface design is somewhat different. Built around a nifty on-line textbook.

Catacomb
Catacomb is a comprehensive, open-source, java-based program for modeling realistic neural networks and virtual environments. It is similar to Simbrain in scope and intent.

JNNS, Joone, Open-AI
JNNS (a java-interface to SNNS) is a powerful freeware java neural network which contains numerous learning algorithms and supported by a large user-base. SNNS is not, however, open-source. Joone is open-source, and its focus is on backpropagation and real-world applications of neural networks.

PDP++
Heir to the PDP simulation package that came with "volume 3" of the original PDP volumes. Not open source.