Having used Windows computers much more than Macs there are certain applications I have come to rely upon which are available for free. The higher availability of great free applications has always been an advantage that Windows has over Mac OS, but there are now many great apps available for Mac OS, some of the ones I feel are particularly useful are listed below:
Office Suite – LibreOffice
Word processor, spreadsheet, presentation and database software with MS Office and PDF compatibility.
http://www.libreoffice.org/
Email Client – Mozilla Thunderbird
Long standing, multi-platform and extremely versatile email client. Not as good as Microsoft Outlook, but probably the best free client available.
http://www.mozilla.org/thunderbird/
Photo Manipulation – GIMP
Extremely rich in features, probably the closest thing to Adobe Photoshop that’s free.
http://gimp.lisanet.de/Website/Download.html
Antivirus – Sophos Home Edition
I am not familiar with the two free antivirus packages I mention here but for features and performance Sophos Home Edition appears to be the highest rated.
http://www.sophos.com/en-us/products/free-tools/sophos-antivirus-for-mac-home-edition.aspx
Antivirus – ClamXav
If you need completely free antivirus software, for business use as well as home use, then ClamXav seems to be the best of the available options.
http://www.clamxav.com/download.php
Media Player – VLC
VLC Media Player is not the prettiest software but it works with almost every format of video and audio. If a friend sends you a video that won’t work, this software might play it.
http://www.videolan.org/vlc/download-macosx.html
Disk Space Management – Disk Inventory X
This very handy application creates a colourful visualisation of every file on your selected disk, enabling you to quickly see what is using up the most space and to remove it if you wish.
http://www.derlien.com/index.html
Application Uninstaller – AppCleaner
Uninstalling applications on a Mac can leave a lot of unwanted files lying around, this app helps to do a more thorough job of uninstalling applications.
http://www.freemacsoft.net/appcleaner/
Deleted File Recovery – EaseUS
This is the closest I could find to a completely free file recovery tool on the Mac that has an easy to use visual interface. This allows you to recover up to 2GB of data for free, which is probably fine for the occasional lost file or folder.
http://www.easeus.com/mac-data-recovery-software/drw-mac-free.htm
Audio Editing Tool – Audacity
If you ever want to modify an audio track this a the perfect tool. You can zoom in on a waveform visualisation of the audio and chop it up as you wish. A noise removal filter is included. If you wish to save files in mp3 format you also need to download a separate encoder (linked from the application download page).
http://audacity.sourceforge.net/download/mac
Archive Extractor – The Unarchiver
A utility that supports decompression of many compressed formats including Zip, Tar-GZip, Tar-BZip2, RAR, 7-zip, LhA and StuffIt.
http://wakaba.c3.cx/s/apps/unarchiver
FTP Client – FileZilla
Not many people will need this, but if you do need a client for FTP, FTPS or SFTP then this a very good free client that has been actively updated over very many years.
https://filezilla-project.org/
As time goes on there will hopefully be some better software to compete with the above, please feel free to mention anything good in the comments.