Several, but my number one fav so far is Battle for Wesnoth. An old school hex tile turn based strategy game. Like something out of the 90's or very early 2000's.
Great art, awesome music, solid gameplay, and runs on a potato.
My best friend and I play it whenever we want a casual chill, play n' chat gaming session.
It runs great on the Steam Deck too with a few interface tweaks.
Base game is free to download and play from their website.
Massive world, tons of loot, an incredible number of classes and abilities to combine, it's such a fantastic game that also has native Linux support.
Veloren is inspired by games such as Cube World, Legend of Zelda: Breath of the Wild, Dwarf Fortress and Minecraft.
You can play single player or multi-player, standalone or use an online server, or even host your own server in a Docker container, or on a Raspberry Pi. Plenty of options!
You start by creating your character, you can collect items for your inventory, you can craft items, there are weapons and combat, you develop skills, can tame creatures, you can trade with merchants, you can socialise, and lost more. There is no single, specific goal or focus, and the idea is to keep exploring and have adventures.
The game is community driven and actually updates quite regularly.
It is clearly no clone of Minecraft. It is fun and adventure!
Cataclysm Dark Days Ahead has been mentioned so I'll add OpenMW to the thread. It's a open source engine rewrite of Morrowind and requires the base game to run Morrowind but it has the potential to be used to create new games and the devs are looking to expand it to allow the creation of ARPGs as well.
Another worthy mention is Endless Sky, it's an open source game inspired by the classic space trading and combat game Escape Velocity.
If you like RTS games similar to Total Annihilation, you should definitely check out Beyond All Reason, it's gorgeous and fun: https://www.beyondallreason.info/
Oof, I have a huge boner for roguelikes, and most of them are open source. My biggest time sink is still Dungeon Crawl Stone Soup, playable online at https://crawl.develz.org/
Duelyst was a very popular online card game that shutdown around 3 years ago. The developers have recently released it into the public domain (via CC0 license).
You can completely selfhost a private instance (repo has a good straight forward guide)
There is a public instance available to try https://duelyst.org/. Though it might be pretty barren.
There is also a closed fork which should have a more active userbase https://duelyst2.com/, the game rules are a little different (draw 2 vs draw1), but should have more users to get a feeling for the game.
The game in a nutshell is basically Hearthstone on a chessboard. It’s very fun and approachable and in my opinion one of the best cardgames right next to MagicTCG :). Hopefully the community for it will grow more and we can have a sort of second renaissance for it :)
I haven't seen any incremental games get posted. They aren't exactly traditional games, but so many of them are open source like Antimatter Dimensions or Synergism. Bitburner is a unique one as an incremental hacking sim, since it relies on actual scripting to grow and automate tasks.
Mindustry is an awesome strategy game that combines Factorio with tower defense.
Sonic Robo Blast 2 Kart (ridiculous name I know) is one of the most underrated games ever. It's a super polished, high quality Kart game with an insane amount of mods and maps. The online isn't that populated but the singleplayer time trial is TONS of fun. If you like hunting for medals, it can be a pretty deep rabbit hole. There's a sequel in development but no release date.
GzDoom is the most popular Doom source port and there's a practically infinite amount of user generated content. If you don't know where to start I highly recommend Doom: The Golden Souls Remastered and Castlevania: Simon's Destiny. They're good enough to be premium games.
Warzone 2100 is an RTS from 1999 that went open source at some point and can be played on just about anything. It's unit design functionality is really cool and I'm a sucker for post-apocalyptic worlds.
OpenRA has open source slightly modernized versions of Red Alert, Tiberian Dawn and Dune 2000. There's also Tiberian Sun-like and Red Alert 2 mods for it :)
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.
I still jump into Quake 3 DeFRaG sometimes. It's a movement game, probably one of the earliest examples of a game / mod where the primary focus is on movement as opposed to shooting or some other mechanic. Its mere existence heavily inspired a lot of source engine movement communities like surf, bhop, kz, etc.
Here's a good video showcasing what DeFRaG movement looks like. Each map is ran on two variations of the physics. One is VQ3 (vanilla quake 3) and CPM (Challenge ProMode Arena, which was originally a Quake 3 mod that heavily altered the physics to make it more fun for professional play). While there's no one DeFRaG game, there's a shitload of open source mods to the original game that modify the physics and allow you to join servers running DeFRaG maps. Some of them even hook up to the online database allowing you to register times without recording your runs and submitting them the traditional way. There's usually a new open source defrag mod rolling out every 3 years or so, and each one builds upon the successes of the previous one. The one I currently use is iDFe which I think came out around 2018 or so? I'm pretty sure there's a new one, and there are other games in the works in both modified Source Engine and Unreal Engine 4 that are looking to emulate the VQ3 and CPM physics for modern engines.
The community is pretty dead, but it rises from the ashes every few years for DFWC (the video I linked above was DFWC 2017). You can always play any one of the thousands of maps in singleplayer too.
Teeworlds. There are some great community made modes for it like FNG and DDrace. Be sure to download it from ddnet.tw to access to extra features created by the community.
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.
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).
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.
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.
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.
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.
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.
Pokemon Auto Chess. Literally what the name implies, a Pokemon auto battler game. Honestly it's really well-polished for something only a couple of people are working on (aside from commissioned sprite artists) and has an active community to go with it.
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.