My preferred operating systems are free software Unix-likes: that's nearly always Linux these days, although I'll happily use FreeBSD and OpenBSD too. I run GARStow or Debian GNU/Linux on my own machines.
Terminal emulator
rxvt-unicode. It's quick and lightweight, and has excellent Unicode support, including selecting characters from both core X and Xft fonts (so it doesn't matter if a font's missing line drawing characters any more, for example).
All my text-based applications live in a single large GNU Screen session, to which I attach from wherever I'm working. Screen's ability to have multiple terminals of different shapes attached to the same session is really useful; I've typically got a few dozen terminals attached to my session.
Shell
GNU bash. I'm actually a fairly conservative shell feature user — I'm just as happy in pdksh or zsh, but I like bash because it uses readline and handles non-ASCII characters properly. (I find it astounding that there's still software around in 2011 that doesn't think languages other than US English are worth bothering about.)
Window manager
My window manager is some combination of Openbox, FVWM and the XFWM window manager from XFCE. I've bounced between the three quite a bit over the last few years; as I write I'm using Openbox, but they all work well, and it's easy to get the same menus and keybindings in all three.
I remap Caps Lock to be a Meta modifier key, and use that for a load of window-manager-related and application-launching shortcuts. (This is how I discovered that the IBM Model M keyboard doesn't respond to Caps Lock-Shift-2 as a combination.) One shortcut launches dmenu for running a single command. I never use the numeric keypad, so the keypad Enter key is bound to launch a new terminal; it's easy to hit accurately.
System monitoring
The one bit of chrome
on my desktop is GKrellM
with most of the meters turned on.
It's handy to be able to see immediately when my network connection is
being hammered, or when I've got new mail.
I'm using the twilite
theme, as it's boring but fairly readable.
Web browser
I use Firefox. It's ridiculously slow and memory-hungry, but it's got a number of useful features that haven't made it into any of the other free browsers yet: decent typography through pango (unlike WebKit browsers), working custom stylesheet support, and a good range of extensions. Extensions I use include Adblock Plus, Greasemonkey, It's All Text!, NoScript and Tree Style Tab. I have some GM scripts that fix various kinds of broken HTML.
I use ELinks when I don't have X available. It's nice being able to bounce between the source and the rendered version, and to view the source of arbitrary URLs without needing to worry whether the browser knows it's a text type or not.
Mail client
Mutt does everything I want: it's text-based, it's quick, it's easy to customise for different accounts, it understands plenty of mailbox formats, and it does GPG correctly.
My customisations include some PINE-like keybindings. A long time ago I used to be a PINE user, and my brain hasn't recovered yet.
Text editor
VIM, usually. I started using this on the Amiga, and these days I use it for pretty much everything; good syntax highlighting and being able to type ex commands when I need to do something complicated are the two key features.
I don't use GNU Emacs much as an editor these days, but it's a great virtual machine for programs that need to deal with text — I always have at least a couple of Emacs sessions open running Gnus and Org-Mode.
Newsreader
Gnus within Emacs. The killer feature is that it'll happily treat mail folders as newsgroups, so I can deal with mailing lists transparently. I'm using the nnimap backend with the Dovecot imapd, since I've got lots of mail folders and nnmaildir's performance is pretty awful.
Calendar
Org-Mode within Emacs. The calendar display is good enough, and keeping everything as plain text means that I can easily synchronise my calendar, to-do list and random notes around using a version control system.
File manager
ROX-Filer. I do some file management at the command line, but for finding things quickly and moving files around, ROX-Filer provides an excellent clone of the RiscOS file management interface, which I happen to like a lot. It handles large directories well, and the filtering and sorting features work really nicely for things like photo management and dealing with MythTV recordings. I use drag-and-drop into applications rather than file dialogs wherever possible.
I wasn't very happy with the loss of the Details view in the ROX-Filer 2.0 series; even after some modification, I still don't find the List view usable, since it completely changes the mechanisms used for group selection and drag-and-drop. My ROX-Filer is patched so it's got an option to make the column views always be a single column wide by default.
Music player
Potamus, my replacement for GNU xhippo (which I also wrote). I'm playing around with the Potamus UI to see what features I do and don't need.
I use envy24control to control my soundcard's mixer (it's an ice1712-based card which has some odd features, so the regular mixers don't work that well). Since I've got a real mixer sitting next to the computer, I don't use the soundcard's mixer that often.
Video player
MPlayer, which copes perfectly with a wide variety of video formats, handles wacky stuff like subtitles appropriately, and has a nice simple keyboard interface.
VLC is also excellent; I use it when watching interlaced content (since MPlayer doesn't appear to do bob deinterlacing), and when I need to switch between audio streams in a file.
Graphics editing
GIMP. No complaints; having never been an Adobe Photoshop user, GIMP's interface makes perfect sense to me.
For rotating large numbers of photos and similar, gthumb is my tool of choice. When I need to script graphical work I'll use GraphicsMagick and NetPBM.
Audio editing
For small jobs, mhWaveEdit — nice snappy UI, and does JACK properly. For multitrack recording and serious editing, Ardour is brilliant.
"Office" stuff
For word processing, I use VIM and LaTeX, since that lets me produce documents that look nice with the absolute minimum amount of hassle. It's hard to beat LaTeX for academic — and especially collaborative — writing, and it's a pretty sad reflection on the software industry that nobody's produced anything in the last 30 years that matches its output quality, or deals with references as easily.
For slides, spreadsheets, drawing diagrams, and dealing with documents in proprietary formats, LibreOffice does the lot. Instant good-quality PDF export is a particularly useful feature.
For generating charts, I use gnuplot; it's one of those tools where pretty any feature I want is probably there, somewhere, if I can navigate my way through the creative help mechanism...
IRC client
Irssi. I've twiddled a lot of configuration settings and created my own theme to make irssi fit into my setup (and brain) a little better. It supports everything I could want from an IRC client, and works nicely with multiple channels in text mode.