Ricci - A Mathematica package for doing tensor calculations in differential geometry and general relativity. - http://www.math.washington.edu/~lee/Ricci/
The Cactus Code - A modular manageable high-performance 3D tool for Numerical Relativity. - http://www.cactuscode.org/
Whisky - A code to evolve the equations of hydrodynamics in curved spacetime (relativistic numerical hydrodynamics). - http://www.whiskycode.org/
Riemann Package for Maple - Package written in Maple for calculating tensor components in General Relativity and performing some abstract tensor manipulation; suitable for calculations in general relativity and for quantum field theory in curved spacetime. Features brief description - http://www.cbpf.br/%7Eportugal/Riemann.html
Riegeom Package for Maple - Package for the mathematical software Maple: abstract tensor manipulation and component calculation in Riemannian spaces; suitable for a variety of calculations in general relativity. Features a short description, examples, downloads for Maple V, and a li - http://www.astro.queensu.ca/%7Eportugal/Riegeom.html
openGR - An open framework for large numerical simulations in general relativity. - http://wwwrel.ph.utexas.edu/openGR/
LORENE (Langage Objet pour la RElativite NumeriquE) - Provides a set of C++ classes to solve various problems arising in numerical relativity and other areas of computational astrophysics. - http://www.lorene.obspm.fr/
GRTensorM - A version of GRTensor II for use with the Mathematica software. - http://www.astro.queensu.ca/~grtensor/grtmma.html
GRTensorII - A computer algebra package for performing differential geometry calculations. Site includes demonstrations of the package's applications to general relativity. - http://grtensor.org/
GRAVLENS - Software for modelling gravitational lens systems; created and maintained by Chuck Keeton at Rutgers University. - http://redfive.rutgers.edu/~keeton/gravlens/
Form Symbolic Manipulation System - A free software package for manipulating tensors (abstract index notation) and other multi-component objects; highly suitable for calculations in general relativity and related theories such as supergravity. Site includes documentation, course material, a - http://www.nikhef.nl/~form/
Cartan: A Mathematica Package for Tensor Analysis - Product information from Ad Infinitum AS about a package for use with the Mathematica software; allows interactive tensor calculations in spacetimes of arbitrary dimension. - http://adinfinitum.no/cartan/
CarpetCode - A mesh refinement driver for the Cactus code; the primary application is the simulation of black hole spacetimes. - http://www.carpetcode.org/