Although there are less commercial games available for Linux than Windows and Mac, there are some good games that run on Linux.
These are some native Linux games that I have tried.
These are available for all Linux distributions.
1. The Battle for Wesnoth
The Battle for Wesnoth is an open source turn-based strategy fantasy game.
2. Extreme Tux Racer
Extreme Tux Racer is a racing game starring Tux, the Linux Mascot.
3. Alien Arena
Alien Arena is a shooting game based on the Quake 2 source code.
These are some browser-based games that can run on Linux.
1. RuneScape (requires Java to be installed)
Runescape is a fantasy free online multiplayer game.