I'm by no means a game developer, but I do like to develop games. By that, I mean I like to put together quick little projects for my kids/self/friends to play around in, but generally have no real idea what I'm doing and it's more about the challenge and fun of it, than producing anything truly professional.
All my games are "released" (shared privately) for free and open source, so I try and use as many free and open source tools wherever I can. I'm not making any money off my games, so I can't really spend any money on them either. The only real exception is that I do use Game Maker Studio 2 which I picked up in a Humble Bundle a few years back really cheap.
This post will be an updated-as-required list of my favourite free tools to help you make your game.
Tools and resources for pixel artists, including tutorials, palette lists, a web-based pixel editor, software recommendations, and more.
Huge selection of 2D and 3D game art under a variety of open licensing for you to use in your hobby and/or production projects.
The Spriters Resource
The Spriters Resource has thousands of sprites and graphics that you can use for inspiration, reference, or to prototype your game. Many are taken from existing games, but there's also a solid selection of custom/modified sprites too. I mostly use it to get ideas and inspiration for animation, or to reference how other people do certain actions and effects.
Universal LPC Sprite Sheet Character Generator
[Gaurav Munjal] has created this absolutely amazing web-based character sprite generator based on the Universal LPC Spritesheet which is a great set of character sprites to get your game going. It's open source and has everything you need to put customisable animated characters into your game with lots of clothing items, weapons, tools, and so on.
RPGTileset.com has thousands of tilesets for both characters and world/environment decoration. They're designed for RPG Game Maker software but I have found they work fine in Game Maker Studio 2 as well. I generally use these just to grab specific sprites from the sets and then modify to suit my game, or just as reference/inspiration, but there's plenty there good enough for your final game too depending on the style you're going after.
Piskel is a web-based application for creating animated sprites from scratch, or modifying existing ones. It lets you create animation frames, layers on each frame, preview the animation in progress, and more.
Seriously great tool that I find invaluable in helping me create new animated characters or open up existing ones to analyze the frame differences better.
Bosca Ceoil is an old-school Impulse-Tracker-style music making program that keeps it really simple, and is ideal for retro games and any game where you just want to quickly put together a classic sounding piece of music. It's about as easy as it gets to use, with a variety of MIDI instruments and tools to build your track, and the ability to export as MID or WAV file.
I love that it's a simple standalone application that you can unzip and use with no installation necessary, and has zero bloat at all.
Bfxr is a Sound Effect Generator that has an online Flash version or like Bosca Ceoil above, has a standalone application you can download and use locally with no installation.
It has a series of pre-designed random sound generators for common actions in games like picking up power-ups/coins, jumping, shooting, getting hit, etc. It then lets you infinitely customise the sound to suit your taste, or create your own sounds from scratch. I can spend hours in this simple little program just playing with all the sliders and coming up with cool sound effects, and adding lots of tiny little sounds to your game is a really great way to add atmosphere with very little performance/size.
Game Maker Studio 2
Despite the amateurish name, GMS2 has grown to be an incredibly competent 2D (and basic-3D) game engine used in a variety of popular indie games. It started out simple, and has expanded to cover pretty much every style of indie game imaginable, from platformers to top-down RPGs to anything else you can imagine. It has basic functionality for 3D and a solid-but-simple physics engine, and is so easy to pick up that you can go from zero-experience to your first playable game in a weekend. Most of that is thanks to the extensive documentation, first-party tutorials, and a large friendly community publishing lots of tutorials and guides, some of which are below:
Probably the most well-known GMS2 Tutorial maker, thanks mainly to his great Platformer tutorial. He also puts out a lot of other tutorials and guides for various aspects of GMS2 though.
Another well-known GMS2 pro, with an extensive collection of RPG based tutorials and more.
Tutorials on card based games, top-down exploration/survival games, and currently putting out videos on turn-based strategy/fighting style games.
Mostly concentrates on Platform Shooters and some individual videos on specific mechanics/features.
More advanced tutorials on specific features like mouse-clickable UIs and re-mappable keyboard controls.