Lakka is the official Linux distribution of RetroArch and the libretro ecosystem. Each game system is implemented as a libretro core, while the frontend RetroArch takes care of inputs and display.
Recalbox is a light embedded system created to run on the raspberryPi ,raspberryPI 2 and on PC x86/x64.
motionEyeOS is a Linux distribution that turns a single-board computer into a video surveillance system.
batocera.linux is an operating system (like Windows 10 and Mac OS) specialized in retrogaming
available for your pc and different nano computers like the Raspberry and the Odroids.
Note that you must own games you play in order to respect legality.