Graphics
2D
Paint.net
The first word in free painting tools. It can do every thing I ever wanted gimp to do, but it didn't take a rocket scientist and a 3rd grader using physics and crayons to explain how to do it. Maybe one of the best features is the nifty User-made Plugins that let it do things like make Icon and Cursor files, as well as DDS and TGA.
DXTBmp
The one thing I don't like about Paint.net is the way DDS files are handled, specificly the alpha channel. Thankfully, DXTBmp makes working with DDS files easy. It has a simple interface, but its power is that you can pass the Image or the Alpha to any painting program, edit it, and then DXTBmp will put it back together as a DDS file. If you work with Civ4 Textures alot, this is a must have, and its free. Ignore the stuff on the download page about Aircraft Simulation stuff, that is just what the program was made for, but it works for all DDS files.
3D
Google Sketchup
This simply ROCKS!! If you ever found yourself sixteen steps into a blender tutorial and wondering why you still haven't been told how to make a square on the screen... this baby is for you. In under an hour, with the help of the in program help and a few free plugins I downloaded from the program's web site, I had a house. A whole house, with windows, doors, interior textures, and a helipad on the roof. Up to that point my experience with graphic design was limited to pixel art in Paint.net.
Misc
AnalogX Capture
Not all games come with a way to capture images of the game and save it to your computer. Well this little, free, program will allow you to take a Screen Shot of anything displayed on your computer.
Text
Word Processing
OpenOffice.org
This program is da bomb. It is totally free and can do everything that Microsoft Office can do, and maybe a few things that it can't.. I don't know for sure, cause one is free and the other costs a bunch of money.
Fonts
High-Soft's FontCreator
Now I don't endorse many things that aren't free, but this thing hooked me with the 30 day trial period. You can make your own languages, designing each letter in whatever painting program and then copy/pasting the image into this program. I still haven't scratched the surface of its true power. On the simplest level, you can replace the normal characters with whatever you want and then use that Font file in any program that you can add new fonts to.
File Parsing
GlobalFind
I don't know if you hate searching for files using the default Windows forlder borwser's search option as much as I do, but I would bet money you will like this one better. It is total Freeware, has a simple interface, and in addition to its fast search for file names, you can also give it regular expressions to search for in the files.
INI Buddy
You can call it a shameless plug, but this is my awesome Configuration INI File editor, it is frekkin great.
WinMerge
If you mod Civ or any other game and you haven't heard of this program, then stop right now and follow this link. You can compare the contents of two files or two directories and it will tell you what is different between the two. Saved me hundreds of hours when combining multiple mods together.
Misc
Computer Management
Belarc Advisor
This is a neat little program I found a few years ago. It will give you a through list of what hardware and software is installed on your computer and it is totally free.
