SuperTuxKart and Mindustry are so much fun!
The ones that come to mind are Beyond All Reason and Battle For Wesnoth.
Mobile on Android: Shattered Pixel Dungeon and Techmino.
I asked this a while ago which is how I discovered Beyond All Reason which has been my FOSS game of choice as of late.
I'd also recommend Naev and Endless Sky (Both are based on the Escape Velocity Series, Naev is getting a 3D PBR renderer in the next release). Mindustry is good fun, actually purchased this one on steam to support the amazing developer. Extreme Tux Racer is a bit of fun and Super Tux Kart seems to get better with every update (did I mention it can run on the Nintendo Switch via homebrew!)
Edit: I forgot about 0ad and Minetest which I used to play a bit of a while back
BAR is great -- Total Annihilation was always one of my favorite games from childhood and BAR feels the most like it compared to other spiritual successors like SupCom/FA and other community projects. I actually tried to contribute a couple commits to the project but I don't think they took them.
Simon Tatham's Portable Puzzle Collection
It's available on Linux, Windows, Android, iOS, and the web.
I play them on my phone to pass time.
Space Station 13.
Too many amazing moments and memories to even count, always more to learn. I love how the open source nature of the game means there's many different servers branching off from each other, running their own custom versions of the game. Smaller servers "downstream" pick and choose which features they want to keep when the upstream servers implement something new.
You might not be aware but there's also a fairly content-rich successor project called SpaceStation 14! Its obviously nowhere near as featureful as 13 is, due to lack of development time but has a very active development community around it.
One of the major (imo) improvements is a move to per pixel "real time" movement instead of the tile movement of ss13, it helps make them game feel much more alive and interactive.
Definitely worth a look for fans of ss13, and its also open source and Linux compatible.
Endless Sky. And AisleRiot Solitaire.
Endless Sky is a great game, and the Android port is solid. If you liked any of the Escape Velocity games then you'll love Endless Sky.
it's not really a game, but openmw
Morrowind was Bethesda's peak moment, so obviously foss engine keeping it alive to this day is awesome!
Cataclysm: Dark Days Ahead Battle for Wesnoth OpenTTD Doom
Cube 2 Sauerbraten, an online FPS. Not many players left anymore though.
Xonotic
Mindustry, Endless Sky, and Unciv.
I still haven't tried it, but I've heard how great Veloren apparently is. It's an MMO voxel game that takes inspiration from Zelda: Breath of the Wild and is written in Rust.
Definetly openTTD. I love trains and its so cool to see your little trains drive around, load some cargo, etc.
FreeCiv is a classic and still fun. rogue and nethack are good, too.
Haven't played it much but for all fans of Thief games there's foss game called The Dark Mod. And I haven't seen it mentioned here, which is a shame.
I am surprised that 0 A.D. is not mentioned.
Although initially unplayable, the game was fun in the mid-to-late 2000s.
I haven't checked it out in a while, but it holds high nostalgic value for me.
DCSS, Minetest and Simon Tatham's Puzzles.
Widelands is a great strategy / building game. The gameplay and UI style is a niche - but that's one of the things I like about it. It's doing something different to most games.
(The gameplay is similar to Settlers 2; before that franchise changed direction.)
[edit] But the open-source game I've spent the most time playing would be OpenXcom-extended, with xpiratez. That game is truly huge.
Unciv is pretty cool, it is Civ 5 but you can play on mobile as well. It was great to have the "One more turn" feel while stuck on a train.
Xonotic.
Formerly known as Nexuiz, until the lead dev sold the naming rights.
supertuxkart, mindustry, unciv and xonotic are my favorites so far
Since no one mentioned yet, Tales of Maj'Eyal deserves some love too. One of the best roguelikes out there..
Xonotic (quake-esque FPS, IMO its like quake and halo had a FOSS child), Minetest (a voxel game engine, multiple games are available for it), and Mindustry (sandbox tower defense) are the only ones ive tried so far
Haven't seen this one mentioned but I have fond memories of Frets on Fire which is a guitar hero clone
Veloren!
Osu. Please save me.
Velorem and Endless Sky!
VCMI - it's re-written from scratch, open source, multiplatform Heroes 3 engine with many improvements and mods manager. It requires some files from the original game though.
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