Scilab is a scientific software package for numerical computations providing a powerful open computing environment for engineering and scientific applications.
Root is an object oriented data analysis framework. Due to the approach of loosely coupled object-oriented frameworks the system can easily be extended to other domains.
Vensim PLE is a version of Vensim that has been designed to lower the barriers to the beginning system dynamics modeler

• Maple -software for symbolic and numeric calculations, scientific visualization, programming, and document preparation.
• Mathematica - a software system for numeric, symbolic, and graphical computations, and CalculationCenter, a mathematical problem-solving environment with a simplified user interface.
• MathCad - an integrated environment for performing and communicating math-related work
• Matlab - for mathematical computation, analysis, visualization, and algorithm development
• Scientific WorkPlace. With Scientific WorkPlace you can create, edit, and typeset mathematical and scientific text. With the built-in computer algebra system, you can perform computations right on the screen.
• Derive can solve a wide range of symbolic and numeric problems. Results can be plotted as 2-D graphs or 3-D color surfaces, enabling different approaches to problem solving.
• LiveMath is a computer algebra and graphing system.
• Macsyma. Symbolic, numerical & graphical mathematics
• Berkeley Madonna is a differential equation solver, and it is currently used for constructing mathematical models.
• STELLA offers a way to dynamically visualize how complex systems and ideas work

Fortran Compilers

• Open Watcom Fortran compiler (free)
  Open Watcom FORTRAN provides a development environment with the tools, SDK's, and libraries you need to create 16- and 32- bit applications for Windows 95/98/Me, Windows NT/2000/XP, OS/2, extended DOS and Novell Netware PC platforms
• Intel® Visual Fortran Compilers for Windows, Linux and Mac OS
  Non-commercial customers can download free Intel® Fortran Compiler for Linux (registration required)
• The Portland Group Fortran compilers for 32-bit x86 and 64-bit x64 processor-based Linux and Windows workstations, servers and clusters.
• NAGWare f95 Compiler Available on a wide range of Unix and Windows platforms. A large number of Fortran 2003 language features are now available
• Absoft Fortran Compiler and associated tools are available for HPC, Linux, Windows and MacOS environments.
• Lahey/Fujitsu Fortran and Linux includes full Fortran 95/90/77 and Fortran for .NET compilers, Visual Studio .NET 2003 Standard Edition, Windows & Web Forms Designers, Graphics package, COM and ADO.NET support.

C/C++ Compilers

• Dev-C++ Compiler (free)
  a full-featured Integrated Development Environment (IDE) for the C/C++ programming language
• Open Watcom C/C++ compiler, (free)
  Open Watcom C/C++ provides a development environment with the tools, SDK's, and libraries you need to create 16- and 32- bit applications for Windows 95/98/Me, Windows NT/2000/XP, OS/2, extended DOS and Novell Netware PC platforms
• Microsoft Visual C++ 2008 Express Edition (free)
  Visual C++ 2008 Express Edition provides easy to use, easy to learn tool for building dynamic applications for the .NET framework as well as native Win32 programs.
• Borland C++ Compiler (free)
  (registration required)
• Intel® C++ Compilers for Windows, Linux and Mac OS
  Non-commercial customers can download free Intel® C++ Compiler for Linux (registration required)
• Microsoft Visual C++ 2005
  Microsoft Visual C++ 2005 provides a powerful and flexible development environment for creating Microsoft Windows–based and Microsoft .NET–based applications. It can be used as an integrated development system, or as a set of individual tools.
• Borland C++ Builder 2006 (C++ IDE for Microsoft Windows)
  (Professional and enterprise editions)
• The Portland Group C and C++ compilers for 32-bit x86 and 64-bit x64 processor-based Linux and Windows workstations, servers and clusters.

Basic

• Microsoft Visual Basic 2008 Express Edition (free)
  Visual Basic Express provides a powerful WYSIWYG visual design surface to quickly and easily create interactive Windows applications.

Java

• Microsoft Visual J# 2005 Express Edition (free)
  Visual J# Express provides a powerful WYSIWYG visual design surface to quickly and easily create interactive Windows applications.

Scientific data plotting software

• Origin
  Professional graphing and data analysis software for scientists and engineers.
  With Origin you can combine presentation-quality graphics, the C language, and the NAG numerical library in one package.
  
• SigmaPlot
  Professional graphing software for scientists and engineers
  SigmaPlot offers seamless Microsoft Office integration, so you can easily access data from Microsoft Excel spreadsheets and present your results in Microsoft PowerPoint® presentations.

Scientific data plotting libraries

• DISLIN (free)
  DISLIN is a high-level plotting library for displaying data as curves, polar plots, bar graphs, pie charts, 3D-color plots, surfaces, contours and maps. The software is available for several C, and Fortran compilers on the operating systems UNIX, Linux, Windows, and more.

An extensive list of free compilers and interpreters for miscellaneous programming languages can be found here.