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/
Gaming
From video gaming to card games and stuff in between, if it's gaming you can probably discuss it here!
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This one is great, I have spent many hours on it!
I'd say Pokemon Infinite Fusion. It's written in Rails and the artwork is done by the community
Veloren
For me it's CDDA, a quite realistic and deep apocalyptic survival game with very frequent updates(on the experimental branch)
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.
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.
Simutrans. It's old but really good. It's really easy to lose 10h or so in it before you notice the time.
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?
osu!lazer
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 Emerald 😉
I am a big fan of Neverball
0.A.D., Veloren and Xonotic are my favorites. Also Sonic Robo Blast 2 is freaking awesome
Xonotic. I even got a server in my region!
Puzzle
- Rocks'n'Diamonds - Digging for diamonds while avoiding boulders and enemies
- Enigma | github - Marple 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
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.
classicube is pretty cool, open source Minecraft classic-like game (so, no crafting or survival aspects, limited world sizes)
0 A.D. is the closest experience to Empire Earth I've had on the FOSS side. Great fun!
0 A.D. and Beyond All Reasons for me ^^