The SigmaPi Neural Network Simulator is designed for time-series processing and neural network research on Unix/X11. Since version 0.5, it uses the LSTM neuron model, the RTRL training algorithm and a heuristic learning rate adaptation based on local update sign-changes. It is GPL-covered, so you can use it for free (read the license for more information)
The current version runs with the Trolltech QT 3.x API and is therefore platform-independent. As soon as the QT3 Windows and OSX Versions are available for free, I will release binary versions for these systems.

SigmaPi is no end-user software. It allows the user to change every possible network parameter, and it won't tell you whether a setting is nonsense or not. To use SigmaPi, you should know how a recurrent neural network works (use my links) and how a LSTM neuron processes information (the manual contains a schematic, since the LSTM neuron of SigmaPi differs slightly from other implementations).
Furthermore, I can't guarantee that SigmaPi is completely bug-free. If something unexpected happens, please mail me. I really need the feedback to improve SigmaPi.