Compartmental models

The following popular neural simulators are available.

Cell models and their simulation are specified with the HOC scripting language, or with GUI tools. The NMODL language allows for adding new components such as new ion channel models. Large user base and many example models are freely available through ModelDB (see below).
GEneral NEural SImulation System . Similar remit and functionality to NEURON. It also has a large user base and is undergoing continual development and improvement.

In addition there are a large number of other neural simulators with similar or more restricted functionality. In alphabetical order, examples include:

HHsim is a graphical simulation of a section of excitable neuronal membrane using the Hodgkin-Huxley equations. It provides full access to the Hodgkin-Huxley parameters, membrane parameters, stimulus parameters, and ion concentrations.
neuroConstruct automates the generation of script files for other simulation platforms, principally NEURON and GENESIS. It provides a framework for creating networks of conductance based neuronal models, visualising and analysing networks of cells in 3D, managing simulations and analysing network firing behaviour. It uses the target platform to actually run simulations.
This was developed originally to model the nerve cells in the vertebrate retina. It has been extended extensively over the years and is now a general purpose simulator for modelling a large number of nerve cells, each with a large number of a compartments. It has 3D visualisation tools for displaying networks.
Nodus is a user-friendly package for simulating compartmental models of single cells, or small networks. It runs only on Apple Macintosh computers.
PSICS (Parallel Stochastic Ion Channel Simulator) is designed to carry out simulation of compartmental models containing stochastic ion channels represented by kinetic schemes. PSICS computes the behaviour of neurons taking account of the stochastic nature of ion channel gating and the detailed positions of the channels themselves. It supports representation of ion channels as kinetic schemes involving one or more serial gating complexes. PSICS is intended to be complementary to existing tools, inhabiting the space between whole cell deterministic models as implemented in NEURON and GENESIS, and subcellular stochastic diffusion models (see MCELL, STEPS and StochSim below).
Simulator for Neural Networks and Action Potentials is a tool for rapid development and simulation of realistic models of single neurons and neural networks. It includes mathematical descriptions of ion currents and intracellular second messengers and ions. In addition, current flow can be simulated in compartmental models of neurons.
This simulator is used to investigate morphologically and biophysically detailed compartmental models of single neurons and networks of neurons. Surf-Hippo allows ready construction of cells and networks using built-in functions and various anatomical file formats (Neurolucida, NTS and others). Surf-Hippo is a public domain package, written in Lisp, and runs under Unix and Linux.
A software tool for neurobiologists to analyse simulated neurons and neural networks. Most of the cell models are abstract but Hodgkin-Huxley models are also included.