I know there have been other questions like "What native games are available?" and they often have issues because they turn into a never-ending list of every game ever released for Linux. Good answers can include: As it currently stands, this question is not a good fit for our Q&A format.
Ie if they completely change how the game works, or it takes the game from a point of not really being playable (eg Gem RB) to being feature complete.
Oil Rush is a real-time strategy game based on group control.
It offers mechanics of a classical RTS combined with a Tower Wars genre: control the upgrade of production platforms as well as their defence forces, and send battle groups of naval and air units to capture enemy platforms and oil rigs.
Phoronix have been harking on about this for months like they're getting a dollar every time they mention it (they probably are), but it does look like a genuinely pretty game.
It's made by Unigine, a company that sells a closed source graphics engine and hardware benchmarks based around the tech-demos they've made with it. Trine is a physics-based action game where three characters allow clever solutions to challenges created by hazardous puzzles and threatening enemies.
The gameplay is based on fully interactive physics - each character's different abilities and tactics can be used to invent new ways to overcome obstacles and save the kingdom!
A hard to classify adventure-creativity game that is—in the words of its creator—about placing blocks while running from skeletons.
Minecraft is a playground where players pursue self-set goals such as mining resources, gathering food, constructing buildings, accessing alternate dimensions, and riding pigs.
Achron is the first game to feature single-player and multiplayer free-form time travel.
It is the world's first meta-time strategy game, a real-time strategy game where players and units can jump to and play at different times simultaneously and independently.
A fun, fast paced shooter built on the Dark Places engine, with many weapons and game modes.