Art and Design
My go-to art program. It's cheap, easy to pick up, and just as functional for artwork as Photoshop (and even supports Photoshop files and plugins.)
My secondary art program. It's free, and I use it every now and then for small art projects.
If I quickly want to mock something up, or just quickly change the position of objects in an image, I use this free image editor written in .Net.
The easiest freeware vector design program I have ever used. I currently use this to design logos.
A small, lightweight freeware font designer. Unfortunately does not import from SVG or allow you to place guide images in the background, so it works best if you are able to place curve and corner points freehand without the aid of sketches.
Audio and Music
Undoubtedly the best free audio editor around.
An excellent free pitch correction/"AutoTune" tool that works with any VST-compatible audio editor (such as Audacity). Using the 'Robotic' preset can get a somewhat GLADOS-like voice, and the "Female-To-Male"/"Male-To-Female" presets can be used as alternatives to voice changer software (if you need female voice fill-ins for a radio play but can't find any, for example.)
A rather good music composition program, and probably the best and easiest to use free one.
Quite frankly, there is no other IDE like Visual Studio, and when Microsoft released the Express versions for free back in 2005, it was a godsend. (Really, this is one of the bigger motivators behind me developing .Net applications.)
I used to be a big fan of Crimson Editor, but I've since gravitated over to Notepad++, and have found it to be an invaluable tool in website building. (If you want it to be easier on the eyes, though, switch the font to Consolas.)
Code Compare is pretty much the best visual diff tool that I've tried so far. Synchronised scrolling? Check. Clear indicators of the location of changes? It literally connects them with a line. Inline editing of files? Yep. Changes are highlighted (blue for edits, green for additions, red for removals) and you can even compare entire folders.
AntiTwin is a free and simple tool for discovering duplicate files.
ImgBurn by Jeff Atwood
An image burner and ripper.
The best free font viewer I've found, DP4 displays all the glyphs in a selected font, complete with Unicode position info. It lists all fonts in a given directory, and not just installed fonts like other font viewers, and sports a clean, uncluttered interface.
A lightweight PDF viewer which can also read PDF formats.