[strong]External Tools[/strong]
GIMP [https://www.gimp.org/]
While a few games can be made without graphics, the majority of modern titles involve some sort of images. Pixel manipulation is a pretty basic standard for creating and optimizing visuals for games. The usual program that professional designers use for this purpose is Adobe Photoshop. But not everyone can afford Photoshop, which is not cheap. For the rest of, there is GIMP. The GNU Image Manipulation Program basically wraps up most of the same functionality as Photoshop into a solid open-source package. I install GIMP on just about every computer I use. Whether I'm just resizing a pic, or painting a texture, its the tool I reach for.
Inkscape [https://inkscape.org/en/]
There's more than one way to make 2D images. While GIMP might be what I use to push pixels, Inkscape is what I use for vector illustrations. Vectors are an alternative approach to visuals, where graphics are devised using mathematically-defined paths instead of mosaic-style pixels. Because vectors are pixel-independent, they scale much better, allowing them to remain crisp and clean no matter what size you view them at. Vectors have traditionally been the favored format of printers, and are the go-to approach for many graphic designers when they create logos or fonts. I'm personally very fond of vectors, and use Inkscape frequently. It is also free-to-use, and available for most of the major platforms.
Blender 3D [https://www.blender.org//]
And now we step up to the realm of 3D. Blender is the open-source equivalent of programs like 3D Studio Max. It's the usual option for modelers and animators on a budget. It also has a unique interface that can be a turn off for some, but is usually appealing to programmers. I've been using Blender for a while, and love it. Once you get over the initial learning curve, you begin to realize that almost anything is possible with this program. Not only can you model and sculpt to prodce game-ready 3D characters, you can also texture, paint, produce and edit video, composite, just an insane number of features. Blender has been around for a while, with a constantly active community. It also has a capable scripting system using Python, and an active community of users who produce additional plug-in tools for it. Highly recommended for prospective 3D modelers and animators. Just be ready for a lot of learning. Like any 3D program, it's not the kind of thing you can pick up in just one day.
Sculptris [http://pixologic.com/sculptris/]
With the increasing popularity of advanced shading techniques like normal mapping, the need for extremely high-detail 3D modeling has risen considerably. Not everyone is looking to make low-polycount models. And frankly, some artists benefit from having a simpler, more streamlined interface. As much as I love Blender, it is a complex piece of software. For those users, there are programs like Sculptris. While Sculptris doesn't feature the complete feature-set that Blender does, what it does provide is a clean, simple interface, and a really nifty adaptive-detail scuplting system. It is very useful for creating high-definition 3D models, and much easier to learn and get into.
Audacity [https://www.audacityteam.org/]
You need to record, edit, or alter audio. Audacity is the program for you. It provides all the tools you need for managing a personal audio studio. You can even combine it with the audio features on a Mac to perform multi-track simultaneous recording from multiple microphones. (I've tested this feature personally, it works like a charm) Most people who know about audio editing likely already have a copy installed.
Musagi [http://www.drpetter.se/project_musagi.html]
This is a music composition project by the fantasitc DrPetter. I strongly recommend poking around his homepage, as he has produced several game-related toosls that are very impressive and useful. He was actually the original creator of Sculptris. Musagi allows you to create sophisticated musical compositions.
Milky Tracker [http://milkytracker.titandemo.org/]
MOD Tracking is an approach to music composition that seeks to use small audio samples as instruments, and then adjust the settings for the playback of those samples in order to generate music. Because it's based on audio samples instead of synthesizers, its playback is independent of hardware. It has been a popular method of composing video-game music for quite some time. Milky Tracker is an active program for creating music in this format, and is available across many different platforms.
Tiled map editor [https://www.mapeditor.org/]
This one is another project that has been around for a while. And it's come a long way in that time. It is now commonly considered to be THE tool for 2D map generation/editing. It is relatively simple, but can do a lot. It allows you to define a tile set, and then use that tile set to create extensive maps/levels. For old-school tile-based games, it is basically a must. It exports all of its creations in an XML format that is very easy to interpret and load. There are several game engines that actively support Tiled's XML format, and can load it natively. For anyone looking to work on 2D tile-based games, this is a very easy recommendation.
Visual Studio Code [https://code.visualstudio.com/]
Visual Studio proper has been the industry-standard for code creation for a while. But Microsoft's own lite alternative is rapidly gaining ground on its big brother, especially in the indie space. Visual Studio Code is a much more stripped-down IDE, paring the experience down to the essential elements. This more minimal approach provides a leaner, more focused program. Code also has much better cross-platform support, being availalbe on all the major operating systems. It's extension feature allows functionality to be added as needed, instead of being bundled in from the beginning. Code highlighting and intellisense round out the package. Many indie and open-source projects have started shifting over to using Code as their default IDE and editor. A great cross-platform code editing interface.