Gaming

Classic roguelikes have the most longetivity for me. Crawl, Brogue, Nethack.

Endgame: Singularity is a fun (and sometimes very frustrating) small strategy game worth checking out.

The Dark Mod is basically Thief but really well done with a solid amount of (fan) missions to choose from. Speaking of I should play some of it again.

Puzzle

• Rocks'n'Diamonds - Digging for diamonds while avoiding boulders and enemies
• Enigma | github - Marble puzzles (and much more) inspired by the classic game Oxyd
• GNU Robbo - Solve rooms (puzzles) with your robot

Space

• Oolite | github - an open-world space opera (inspired by classic game Elite)
• Kobo Deluxe - 2D scrolling space shooter, destroy star bases with your ship
• Open Tyrian - Arcade-style vertical scrolling shooter

shattered pixel dungeon

Simutrans. It's old but really good. It's really easy to lose 10h or so in it before you notice the time.

I like supertuxkart and minetest

Not quite what you are asking for, but here's a list of source ports of commercial games, most of which have Linux ports.

Oh and I'll single out The Ur-Quan Masters as an older source port of Star Control II. Old enough that the port itself is nostalgic for me, although it's still being updated by the looks of it.

Battle for Wesnoth is a personal favorite of mine that I haven't seen mentioned elsewhere in the thread. It's a pixel art, hex-grid turn based strategy game with fantasy armies. It's mixed with mild RPG elements, and there's tons and tons of campaigns and fanmade content accessible directly through a mod browser in game.
The other games I enjoy that I see being mentioned here are in the same vein. BAR, Warzone 2100, OpenTTD. And the open mods based on the STALKER engine, like Anomaly. I love those.

There are a few open source game projects I follow. I suppose the most famous one is the Freespace 2 source code project. Although it didn't start open source, the original devs open-sourced it later. It has great support, and a great modding launcher called Knossos. To play the game, even with the source code, you either need the original disks or a copy of the installer from GoG, but it's really cheap. Getting it working on Windows is pretty easy, but Linux is only slightly more complicated. (Fortunately, there's a new launcher that makes it way easier).

If you're interested, let me know.

If you didn't already suggest it, I would have suggested Veloren!

OpenTTD is a great open source clone of the transport tycoon game. And boohu is an awesome ASCII coffeebreak roguelike.

It's old but I always really liked WARSAW it was/is a quake3 port but with more cartoony outline graphics similar to Borderlands style.

Xonotic. I even got a server in my region!

I'd say Pokemon Infinite Fusion. It's written in Rails and the artwork is done by the community

OpenTTD is my drug. I'm addicted

Dungeon Crawl Stone Soup for me. A classic roguelike with active community and regular updates as well as several forks. It also has a good amount of playable races. From classics like elfs or orcs ~~and dwarves~~ (RIP Mountain Dwarves you were too good for this game) to funky races like Vine Stalkers (sentient parasitic plants) and Armataurs (centaurs but with armadillo parts instead the horse ones) to cats and octopuses.

And the gods you can worship in the game are also very diverse. How about a slime god? Or someone who wants you to wear as much cursed equipment as possible in exchange for knowledge? Or maybe the one who wants everything to move veeery slooow and rewards you for killing mobs that are faster than you?

Only one that comes to mind is Lugaru. The creator had this weird legal battle where someone stole the game, ported it to iOS, and the thief claimed because it was open source he was allowed to sell it.

classicube is pretty cool, open source Minecraft classic-like game (so, no crafting or survival aspects, limited world sizes)

osu!lazer

I'm surprised to not see Flare RPG mentioned. It's nothing groundbreaking on its own, but it's actually got two nicely fleshed out campaigns, and tooling for people to make new ones. It's a nice, fun, FOSS single-player RPG, and it's great if you want that old fashioned Diablo feel.

Another vote for Endless Sky here as well, it's just excellent, and surprisingly expansive.

Oh~ this game looks like someone was really disappoined by how cube worlds dev killed the release on steam i guess. Thanks for that, i will check it out. tl;dr Game was gutted on steam release but so much more was already done, promised and/or teased.