I hope this list is useful to newcomers and veterans alike.
Modified 5/31/16.
Graphics:
Spriters Resource: Graphics ripped from various commercial games. Find animated sprites, tilesets, and more here!
Paint.NET: A nice all-around editor for Windows. Less powerful but much more user-friendly than GIMP.
Aseprite: Great pixel art-focused editor with a palette and animation frames. Great for making tilesets and sprites from scratch.
See also:
Pixel Prospector's list of tools and royalty-free graphicsSounds and Music:Sounds Resource: Sounds ripped from various commercial games.
Freesound: A bunch of real-world sounds people have recorded.
Audacity: All-purpose audio editing tool. Useful for changing music volumes and tweaking sounds, and converting between formats.
There are lots of ways to obtain music: youtube downloader sites, video game remix sites, soundcloud, and many more you can find through googling.
See also:
Video Game Caster's list of royalty-free music and soundsOther:Jtool and RMJ: Useful for testing out jumps without having to compile your whole game, and also for designing entire needle screens.
map2gm: Eliminates having to copy objects over manually into Gamemaker if you use RMJ or Jtool to make needle screens.
Crystalline: An essential tool for working with Gamemaker particles. Particles are a great way to add flair to your game!
See also:
the tools board has a few more fangame-specific tools.