OpenRCT2, eDuke32, the various Doom and Quake games

Also ScummVM is open source and supports many games

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.

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.

I like supertuxkart and minetest

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

0.A.D., Veloren and Xonotic are my favorites. Also Sonic Robo Blast 2 is freaking awesome

Pokemon Emerald 😉

Xonotic is a fun quake-like shooter. Highly recommend.

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.

Xonotic. I even got a server in my region!

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

osu!lazer

Cataclysm: Dark Days Ahead

Tremulous - The game was so fun back then (like 10 years ago ?) I guess it's a dead game now.

For me it's CDDA, a quite realistic and deep apocalyptic survival game with very frequent updates(on the experimental branch)

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.

Unciv! Remake of civV for desktop and Android.

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

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

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.

I am a big fan of Neverball

0 A.D. and Beyond All Reasons for me ^^