Gaming

OpenTTD is my drug. I'm addicted

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

0 A.D. is the closest experience to Empire Earth I've had on the FOSS side. Great fun!

Aside from the other choices already mentioned (especially Doom stuff, FreeDoom ftw) any of the free games derived from the S.T.A.L.K.E.R. games and early builds, mostly Anomaly and Lost Alpha. There are also a few stabilized versions of the Build 1935 alpha out there which are worth playing and probably a bit more approachable for most people.

Xonotic. I even got a server in my region!

I like supertuxkart and minetest

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

Surprised it's not mentioned here, but Bzflag.

Super fun tank shooter game that doesn't take much to run, and reminds me of a cross between the very old bolo game and Mario kart's battle mode.

I am a big fan of Neverball

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.

osu!lazer

If reverse-engineered Nintendo games count, then Super Mario 64 and Pokemon Emerald whose engine is technically open source.

EDIT: Minecraft Beta 1.7.3 has been reverse engineered multiple times too.

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.

Pokemon Emerald 😉

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.

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?

shattered pixel dungeon

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.

Veloren

There's not a whole lot of activity around it these days, but Zelda Classic is an engine for Zelda 1 with a number of additions and improvements, that allows for custom maps, tilesets, scripts, items, enemies, etc. etc.

I've whiled away an unreasonable amount of time on quests that are on par mechanically and quality-wise with Link's Awakening and the Oracle games. Shame I can't get the tarball to work properly on Steam Deck, it's a great fit for that hardware.

Terminal games:

Adventure - A classic adventure game. (In the BSDGames package) Hack - The game that inspired NetHack. (In the BSDGames package) Greed - A game where you go through a number field, eating the numbers. It's hard to explain but very fun. Rouge - It's nice to go back to the classics. I like Hack a bit more though.

Non-Terminal Games:

Secret Maryo Chronicles - It's like Super Mario Bros. Alien Arena - Kind of like natural selection. Urban Terror - Kind of like Counter-Strike Warsow - Kind of like Quake. Xonotic - Like Quake again.

I think that's all I played back in the day.