I will be adding links to Open Source software sites where you can search, browse and download free software to replace or add to your existing commercial software. I will add personal reviews to software that I have used and can personally recommend.
Definition: Open Source software has a very specific definition, but basically it must be distributed for free and other people must be allowed to modify or add to the software.
Software I have used and can recommend
Mozilla Firefox – A free open source web browser with millions of addons to increase functionality.
OpenOffice – A free open source alternative to Microsoft Office, powerful and versatile.
7-Zip – A free open source archive tool. Formats 7z, ZIP, GZIP, BZIP2 and TAR are supported fully, other formats can be unpacked.
Revo Uninstaller – A free uninstaller, useful for comprehensively removing those stubborn software installations!.
G.I.M.P (GNU Image Manipulation Program) – A free, open source and extremely powerful image manipulation suite.
Audacity – A free, open source audio editor and recorder.
VLC Media Player – A free, open source media player for most formats.
DAZ3D Studio Pro – A free, incredibly powerful 3D figure illustration/animation application with hundreds of expansions and addons (most are free but a lot are payware).
This list is NOT exhaustive obviously and only contains software I have used and can recommend personally, with a quick search of wikipedia, you can find literally thousands of free and/or open source software applications.