Here's my list. Note that some of this I haven't had a chance to use yet but I would consider them necessary for their particular specialty. My list is designed mostly around quality cheap or freeware applications:

Modeling and/or animation: Blender, Milkshape, Wings3D, Ultimate Unwrap3D, and fragMotion
(Wings3D should take a more prominent place in a 3DGS developer's toolbox given it features FBX import/export and new beta versions of 3DGS feature this as well. The fact that our FBX allows up to 4 bones per vertex is great. fragMotion will soon feature FBX, too)

2D: Paint.NET (with DDS plugin), Inkscape (for vector graphics and PDF creation), Wood Workshop
{These two free programs continue to amaze and grow in power with each successive update. They also use a traditional Windows UI, so none of that esoteric GIMP nonsense. However, GIMP is a nice program, as well and should also be considered. Wood Workshop is a freeware texture creator esp made for wood textures, although it can be used to make just about anything if you use your imagination)

Audio and video: Kristal Audio Engine, Audacity, Exact Audio Copy, burnatonce, dbPowerAmp (with OGG encoder), Virtualdub, and appropriate video encoders

Misc: Pencil/pen, paper, lots of caffeine, and a good selection of music with headphones, FontGenerator, Easy Particles 3, CRED tool, SMEE, Dan's Arch-E 3DGS arch/stairs generator, Inno Setup with ISTool, OpenOffice or Atlantis Nova word processor, Adobe Reader, and of course 3DGS