Quantum GIS (QGIS) is a user friendly Open Source Geographic Information System (GIS) that runs on Linux, Unix, Mac OSX, and Windows. QGIS supports vector, raster, and database formats. QGIS is licensed under the GNU General Public License. QGIS lets you browse and create map data on your computer. It supports many common spatial data formats (e.g. ESRI ShapeFile, geotiff). QGIS supports plugins to do things like display tracks from your GPS. QGIS is Open Source software and its free of cost (download here).

GNU Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command line interface for solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with Matlab. It may also be used as a batch-oriented language.

Scilab is a scientific software package for numerical computations providing a powerful open computing environment for engineering and scientific applications.

Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices, and tensors. Maxima yields high precision numeric results by using exact fractions, arbitrary precision integers, and arbitrarily precision floating point numbers. Maxima can plot functions and data in two and three dimensions.

wxMaxima is a cross platform GUI for the computer algebra system maxima based on wxWidgets.

SciCraft is a powerful open source data analysis software with an easy-to-use graphical user interface.

YACAS is an easy to use, general purpose Computer Algebra System, a program for symbolic manipulation of mathematical expressions. It uses its own programming language designed for symbolic as well as arbitrary-precision numerical computations. The system has a library of scripts that implement many of the symbolic algebra operations; new algorithms can be easily added to the library. YACAS comes with extensive documentation (320+ pages) covering the scripting language, the functionality that is already implemented in the system, and the algorithms we used.

R Project is a free software environment for statistical computing and graphics. It compiles and runs on a wide variety of UNIX platforms, Windows and MacOS.

The R Commander: A Basic-Statistics GUI for R.

SciViews is a collection of freely downloadable software for data acquisition and statistical analyses in sciences.