SparkyLinux "Game Over", live.linux-gamers.net and the Fedora Games Spin are "boot 'n play" DVDs providing Linux and a collection of ready-to-play games.
The Linux Game Database list FOSS games and games that run on FOSS platforms. There are also lists of FOSS games at the Open Directory Project, Wikipedia and Reddit.
Many proprietary games have native Linux ports: First Person Shooter games from id software, Unreal Tournament, many Quake variants, Neverwinter Nights, large catalogues at Tux Games, Linux Game Publishing, Desura, indievania, the Humble Bundle Store, Steam and various ports by Ryan C. Gordon. Indy games also include Linux ports when participating in the regular pay-what-you-want Humble Bundle promotions.
The Unity game development toolkit has supported native Linux as a target since version 4, and consequently many of the games developed with Unity are or will be available on Linux.
Information on finding, installing and playing games under Linux is available in the Linux Gamers' FAQ including another list of Linux games. PlayDeb.Net makes installing games easy on Ubuntu Linux.
Linux Game Cast is a YouTube channel about gaming on Linux. Gaming On Linux is a website with Linux gaming news.
You can also run proprietary games on open source platforms using Wine, Crossover Games, Cedega, ScummVM, DOSBox and many other emulators and game engine recreations. The Wine Application Database lists the status of Windows games running on Wine and ProtonDB lists Windows games running on Proton, the fork of Wine maintained by Valve Software for Steam running on Linux. There is also a list of Open Source Game Clones.
There are also many Open Source games for Windows.
Free and Open Source software has a multitude of applications in game development. SourceForge has a list of games hosted there.
devkitPro supports development on GameBoy Advance, GP32, Playstation Portable and GameCube.
"Introduction to Computer Games" (PDF), a presentation. Please contact me if you would like me to present this talk and demonstration again.
Comments and suggestions welcome at firstname.lastname@example.org.