2D Graphics / Image Editing
GIMP - Free. Works slightly better in Linux than Windows IMO. Lots of features. Slightly weird UI. Great support for DDS files. Strong all round open source tool.
Photoshop CS2 is not actually freeware. Removed from list - apologies.
Genetica Texture Viewer - Allows you to open and tweak Genetica textures. You can use the default library of free textures, change the random seed setting to generates some variations and use them anywhere you want to. Download Texture Packs.
Wood Workshop - Free seamless texture generator for wood textures.
XSI SoftImage Mod Tool - Free 3D modelling tool for modders. Cut down from real software. A bit old now, and has a few bugs you may need to get around if unlucky. A bit more like 3DS Max than Blender - which I get on with better. Exports to DAE which works with the GMT (be sure to check export normals), and also FBX.
NikSkope - While primarily for the 3D Elder Scrolls games, Nifskope supports OBJ format and has tools for UV Mapping, Material / Node editing and more. Also useful for converting content from Oblivion/Skyrim mods!
TextureMate - A good texture library of over 2800 textures.
CGTextures - The best texture library on the web IMO (LordYig!), requires a free account creation to unlock high resolution image and a limit of 15MB downloads per day. Thousands of images, high resolution available, lot of category to choose from, high quality stuff, regular updates with dozens and even hundreds of new textures every week...
Media College - Free Sound FX - A collection of nicely organised free sound effects that you are free to use any way you like (apart from reselling them!).
Sound Bible - Another database of sound files. This site is split into two sections, Royalty Free Sounds that you can definitely use in your mod, and 'Sound Effects' - which are all listed with different licences, but nearly all of them are simply Creative Commons or an attribution licence (so you might need to keep a list of the usernames of the people that made the SFX).
Partner's in Rhyme - Royalty free music and sound effects. Check the license for each sound before using though.
GR Sites Free Sound Effects Archive - Free for personal / non-commercial use.
Philharmonia Orchestra Recordings - Public domain recording of instruments by The Philharmonia Orchestra.
Free Music Archive - Mahric: It's where I got the music for my latest mod. The quality is good, but be sure to check the conditions it is released at. Almost all I saw where free for non-commercial use and only required to credit the author of the music piece.
Genetica - Standalone seamless texture editor. LordYig: Another very good software, some of it's functionality are unique when compared to filter forge. Easier to use and see what you are doing than FilterForge, at least in the begining, IMO.