This is way for people to discover packages that they wouldn't otherwise know about. These programs are listed according to their purpose.
The first section lists user-friendly programs. The second section lists programs that are suitable for experts or people who are learning to become experts.
User-Friendly Programs for Everyday Desktop Use
All of these programs are graphical and intended for the user who doesn't have the time or incilination to study a lot of technical documentation.
Graphical Environments
GNOME, KDE, Xfce
Web Browsers
iceape (mozilla), iceweasel (firefox), konqueror (kde), epiphany (gnome)
File Managers
nautilus (gnome), konqueror (kde), thunar (xfce)
Text Editors
kate (kde), gedit (gnome).
Adobe PDF Readers
kpdf (kde), evince (gnome), xpdf (ugly X11 pdf reader)
Password Managers
kwalletmanager (kde), revelation (gnome), jpilot with jpilot-plugins (specifically, keyring, for use on the desktop and on PalmOS devices)
Resize the Screen (800x600, 1024x768, 1400x1050, etc)
Screen Resolution (gnome, found in the Desktop/Preferences menu, and included in the gnome-control-center package), kcontrol (provides "KRandRTray"), xfce settings manager (xfce4-mcs-manager).
Programs for Experts and System Administrators
These programs may be less user friendly, require use of the command line, or might harm your installation in some way if you don't know what you're doing.
Compile C/C++ programs from source code
build-essential
Other programming languages not covered by build-essential
python, perl, g77 (fortran), clisp (common lisp), ocaml, ghc (haskell), hugs
scheme: there are over 50 implementations of scheme, not all of which are (or deserve to be) in debian.
Install Packages from Source
apt-src to compile pre-existing debian packages from source and remember changes that you make even after the official packages are updated.
checkinstall to quickly make a .deb out of almost any 3rd party package.
kernel-package to compile the linux kernel from source and make a .deb out of it.
linux-source-* install the source code to linux in /usr/src/.
module-assistant to automatically compile and install out-of-tree kernel modules like ndiswrapper.
Make sure that daily/weekly cron jobs run even if your computer is off at the prescribed time
anacron
Get rid of old or unwanted files and packages
deborphan (includes orphaner), cruft, debfoster
Control what modules are loaded in the kernel
modprobe will add/remove a module until your computer shuts down.
modconf will add a kernel module and make it stick.
Window Managers that Make Windows Fill the Whole Screen
ratpoison, ion3
Make a Program Continue to Run After You Log Out
screen (c-a d to detatch), nohup
Make a Program run a Low Priority (so that it doesn't slow down other programs)
nice
DHCP Clients
dhcp-client, dhcp3-client, dhcpcd
Browse the World Wide Web in a Terminal
lynx, links
Use the mouse in a Terminal
gpm
Wireless (802.11)
wireless-tools (iwconfig), ndiswrapper (use windows wireless drivers), linux-wlan-ng (if your card/usb dongle uses a prism2 chipset)
Issue/Bug Tracker (alternatives to Bugzilla)
mantis, otrs, request-tracker, roundup, trac