Free (Libre and/or 'as in beer'.) software.  

This list is what I use on Windows machines.  Linux users probably already have them or can install them from their distro's repository.  I've listed the name of the application, what it would be the equivalent of and the website you can download it from.  These applications support all or most of the 'standard Microsoft' file types and more open standards in many cases.

Firefox replaces Internet Explorer – www.mozilla.org
Thunderbird replaces Outlook or Mail – www.mozilla.org
Opera replaces Internet Explorer – www.opera.com
Audacity is an audio file player/editor - http://audacity.sourceforge.net/
OpenOffice.org replaces Office – www.openoffice.org
VLC replaces Media Player – www.videolan.org
PuTTY for remotely logging onto other hosts on a network - www.chiark.greenend.org.uk/~sgtatham/putty/
Xming replaces Exceed for running X apps in a Windows environment - www.straightrunning.com/XmingNotes/
PhotoRec data recovery application - www.cgsecurity.org/wiki/PhotoRec
Strategy game Battle for Wesnoth - www.wesnoth.org