This is a list of my favorite open source software for Linux. It's organized into categories in the hopes that it may be useful to other people searching for certain kinds of software.
At the moment this list entirely lacks a multimedia production section, as I have yet to find any video editors, audio mixers, or music production applications that are both (relatively) painless to get up and running, and offer sufficiently advanced features for my needs.
Internet
Web Browser
Firefox — A good tabbed browser with support for extensions.
Instant Messenger / IRC Client
Pidgin — A multi-protocol IM client. Supports AIM, MSN, Yahoo, Jabber, etc. and IRC. Check the website for a full list.
FTP Client
gFTP — A simple, straight-forward graphical ftp client that doesn't get in your way.
Office
Office Suite
Open Office — A robust office suite.
Word Processor
AbiWord — If you're not looking for the bulk of an entire office suite, and just want a word processor, this is excellent.
Multimedia Playback
Video Player
VLC Media Player — Straight-forward to use, plays nearly every video file under the sun, plays DVD's, and doesn't have any annoying frills. It could afford to be prettier, but that's about it. The best video player I've found on any platform.
Audio/Music Player
Rhythmbox — Similar to iTunes. This is my primary music player.
Graphics
Paint Program
The GIMP — Essentially Photoshop for Linux, but less powerful. Sufficient for my purposes, though.
MyPaint — Powerful brush system, infinite canvas, minimalist interface. Fantastic for sketching.
Vector Graphics Program
Inkscape — A good vector graphics program.
3D Animation Suite
Blender — It's lacking in some areas, and it can be a bit daunting to new users, but by-and-large a capable app.
Programming
Editor
gedit — By default a bare-bones text/code editor, but it has a flexible plugin system that lets you turn it into just about anything you want. Simple, extensible, easy on the eyes.
Build System
SCons — Simple, elegant, powerful, scriptable, and extremely cross-platform. It's like Make if Make had been made in heaven. By geniuses.
Code Documentation
Doxygen — A widely used code documentation system.
Revision Control
Bazaar — My favorite distributed revision control system.
Subversion — My favorite centralized revision control system.
Graphical Debugger
KDbg — The friendliest and nicest graphical debugger I've found for Linux so far.