Homebrew

"Homebrew" is a bit of a misnomer. Traditionally, if a game development studio wanted to make a game they would obtain debug hardware from a console manufacturer and use that to produce a product to be sold at retail. A hobbyist interested in running their own code on a console may run into difficulty, since doing so would require bypassing licensing requirements and anti-piracy measures. Just like brewing your own beer at home, it's technically not illegal to run your own code on hardware you've purchased, but likewise it's not exactly commercially viable either.

In any case, open development tools for many retro consoles have made homebrew easier than ever. The following is a non-exhaustive list of homebrew titles.

Sega Master System / Game Gear

Heroes against Demons An impressive Puzzle Quest style game.
Mai Nurse If Dr. Mario was not shackled to Nintendo consoles would he be a cute anime girl? Evidently, yes.

Sega Genesis / Mega Drive

Miniplanets A fascinating puzzle platformer with a psuedo-3D view.
Old Towers Platformer with a very modern-feeling style and control.
Irena Genesis Metal Fury An R-Type style horizontal schmup.

Sega 32x

Sonic Robo Blast 32x An ambitious port of the classic Sonic fangame to Sega's misbegotten half-console.