GNU Octave!

Wolfram Alpha is a "Computational Knowledge Engine" - different from a search engine, it answers factual queries directly by computing the answer from structured data, rather than providing a list of documents or web pages that might contain the answer.

MATLAB is a numerical computing environment and programming language. Maintained by The MathWorks, MATLAB allows easy matrix manipulation, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs in other languages. Although it is numeric only, an optional toolbox uses the MuPAD symbolic engine, allowing access to computer algebra capabilities. An additional package, Simulink, adds graphical multidomain simulation and Model-Based Design for dynamic and embedded systems. »

Mathematica is a computational software program used widely in scientific, engineering, and mathematical fields and other areas of technical computing.

Scilab is a scientific software package for numerical computations providing a powerful open computing environment for engineering and scientific applications. Scilab is an open source software and includes hundreds of mathematical functions with the possibility to add interactively programs from various languages (C, C++, Fortran…).It has sophisticated data structures (including lists, polynomials, rational functions, linear systems...), an interpreter and a high level programming language.

Spyder (previously known as Pydee) is a free open-source Python development environment providing MATLAB-like features in a simple and light-weighted software, available for Windows XP/Vista/7, GNU/Linux and Mac OS X.

Julia is a high-level, high-performance dynamic programming language for technical computing, with syntax that is familiar to users of other technical computing environments. It provides a sophisticated compiler, distributed parallel execution, numerical accuracy, and an extensive mathematical function library. The library, largely written in Julia itself, also integrates mature, best-of-breed C and Fortran libraries for linear algebra, random number generation, signal processing, and string processing. »

Online math solver, equation library, graphing calculator and science/engineering problem helper.Calculate multiple equations at once, Edit existing formulas and Create new ones, Compute large numbers of values, Plot graphs, Link your results, Solve full problems and Share worksheets with your friends.

wxMaxima is a document based interface for the computer algebra system Maxima. wxMaxima uses wxWidgets and runs natively on Windows, X11 and Mac OS X. wxMaxima provides menus and dialogs for many common maxima commands, autocompletion, inline plots and simple animations. wxMaxima is distributed under the GPL license.

FreeMat is an environment for rapid engineering and scientific processing. It is similar to commercial systems such as MATLAB from Mathworks and IDL from Research Systems, but is Open Source.

MathStudio, formerly SpaceTime, is the most comprehensive math app available for mobile devices. Whether you need a simple calculator to do your finances or a replacement for your TI graphing calculator, MathStudio is the most powerful and versatile calculator available on the App Store and Android Market.

Xcos is a graphical editor to design hybrid dynamical systems models. Models can be designed, loaded, saved, compiled and simulated.