Note on what was updated: Multimedia players.
This is intended to be a work in progress, so I hope we all contribute to it. Please post your applications, and I will add it to the first post.
All the distributions come with a set of very useful applications, but sometimes the default ones aren't the best out there. It's a wonderful thing we can change them, or add new ones (free of charge) using the package manager that comes with the distro. Mostly Open Source Software. Some of these applications are cross-platform . Another detail to keep in mind is that most of them will work with any distribution. Regardless of the desktop. However, some of them need to replace libraries, which will affect other applications, or even to change the desktop from KDE to Gnome for example. Which could completely change your current settings. I'm posting the website of the developer so if your package manager doesn't have it in it's repository, you can get it from there.
Browsers/Internet/Messengers
Flock is a browser with social networking built into its user interface.
Dillo is a light browser for slower computers and embedded systems.
aMSN is a free open source MSN Messenger clone.
Kopete is a multi-protocol, free software instant messaging client.
CD/DVD/authoring, burning, backup.
K9Copy is a free, open source DVD backup and DVD authoring program.
K3b - The CD/DVD creator for Linux.
Educational Children Games
Childplay
Gcompris
Graphics
GimPhoto is a modification of (GIMP), intended to replicate the feel of Adobe Photoshop.
Blender is the free open source 3D content creation suite.
Hardware Information/Benchmarking
HardInfo Similar to PCWizard, details installed hardware, included basic benchmarking tools.
lshw extracts detailed information on the hardware configuration of the machine.
Networking Tools
SSH clients which use the secure shell protocol:
PuTTY
OpenSSH
Dropbear
Office/Word-processors/Editors
KOffice is an office suite for KDE.
OpenOffice is a cross-platform office suite.
LyX The Document Processor.
Celtx Free screenwriting software.
Online resources for more Linux Applications:
http://www.opendesktop.org/
http://linuxappfinder.com/alternatives
Multimedia players.
aTunes Supports portable players, or anything that could be mounted as a file system; includes a cd ripper tool.
Banshee Music manager that Sync your music and videos to your G1, iPod, or other device.
VLC The cross-platform open-source multimedia framework, player and server.
Smplayer: Multi-platform front-end for mplayer.
Exaile: music manager and player for GTK+
System maintenance:
BleachBit The privacy and disk space cleaner for Linux.