The simulator used to referee Corewar battles is called MARS, the Memory Array Redcode Simulator. New players should note it's easier to find help if you're using one of the most popular simulators, either CoreWin or pMARS.
Will 'Varfar' has written Which MARS? where he compares how various simulators operate. Essential reading if you have an interest in MARS internals.
Stand Alone Simulators
pMARS 0.9.2 is the official Redcode simulator of rec.games.corewar and features a command line user interface and debugger. Full source code is available.
A.R.E.S. 2.35b by Harald Wirth. A MARS for Windows, with IDE, editor and debugger. ARES has experimental extensions allowing stacks, absolute addressing and console i/o.
nMars 0.9.5 is Pavel Šavara's MARS, complete with IDE, editor and debugger for either the .NET Framework or Mono.
Redcoder 0.6 is a sneak preview of a simulator being written by Will 'Varfar'. Uses a command line user interface.
exhaust 1.9.2 is M. Joonas Pihlaja's lightweight Redcode simulator, designed to be easy to embed into applications.
PyCorewar 0.2.0 by Jens Gutzeit is a Python library for simulating, debugging and benchmarking Redcode.
fmars 0.0.207 (fast MARS) is Michal Janeczek's software used to generate a customised, embedded Redcode simulator.
Simulators for Older Standards
XRK 1.71 by Marco Pontello, a simulator for the first Redcode standard - ICWS'86.
The Historic MARS Archive is a collection of Corewar implementations from the past.
CoreLife is a variant of Corewar played on a 2 dimensional grid.