The source code for open source software programs is public and licensed under a Creative Commons license. This means that the code can be freely copied, edited, and redistributed. Open source software is often free of cost, and thanks to an army of hobbyist programmers, open source software packages are often just as good as paid alternatives. For more information on the open source movement, visit the following website:
The Basics
While major operating systems like Windows and Mac can be expensive, many people prefer the open source alternative Linux.
While some programming languages are proprietary (SAS, MATLAB), many programming languages are open source. The best open source programming language is probably Python, while R is an Open Source programming language specifically for statistics applications.
Microsoft Office can also be very expensive, so Open Office may be worth a look.
The Sciences
Science-based applications like Climex and ArcGIS can both be very expensive, but open source alternatives like Wallace and QGIS respectively, are both high-quality alternatives.
The Arts
3D digital modeling software can range from hundreds to tens of thousands of dollars, but Blender is a high-quality open source alternative to these expensive platforms.