https://github.com/wesnoth/wesnoth

Wesnoth is one of those games where once you start playing, you fall into a time warp and lose hours before you know what happened.

Super Tux Kart is a classic

Minetest and Mindustry are two of my favourites. It's a bit complicated to find a good combination of Minetest mods though.

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Beyond All Reason (RTS)

These get mentioned a lot:

• Mindustry
• Unciv
• Shattered Pixel Dungeon
• Battle for Wesnoth

Veloren!

Endless Sky. The save game is a text file. Save a file on the mobile app (F-Droid), and on the PC (Flatpak), and note the last line. This is the line you must swap to transfer the save file. It is the first game I have played on both practically. The game mechanics are different between the two and you need to alter your strategy accordingly. On mobile, I travel with a ship setup for boarding pirate vessels and never target enemies directly; all of my guns are automatic turrets. I just use a fast ship and travel with a large group of fighters. It is more of a grind on mobile, but it can be used to build up resources and reserves. The game is much bigger than it first appears to be. You need to either check out a guide or explore very deep into the obscure pockets of the map.

I haven't seen OpenTTD mentioned yet: https://www.openttd.org/
If you like it you may also check out OpenRCT - although this one needs original game files from RollerCoasterTycoon (a few bucks on Gog or Steam)

Wesnoth, SuperTuxKart, and Xonotic

Cataclysm dark days ahead

I have to second the mentions of OpenTTD, Battle for Wesnoth, Ur-Quan Masters and Nethack.

I'd also like to add:

• Widelands: A Settlers 2 clone.
• Chromium B.S.U.: A top-down scrolling shooter. Don't let any enemies pass. Perfect if you need 5 minutes of adrenaline.
• Scorched 3D: It's Scorched Earth, but 3D.
• Frozen Bubble: Hard to describe. It's a bit like Dr. Mario.
• GL-117: 3D air combat. The graphics are "a bit" dated, but the game is a lot of fun still.
• Kobo Deluxe: A 2D action-puzzler. It doesn't have the most stunning graphics, but it sure is fun to play.

Then there are also some open-source re-implementations of commercial games (that need the original game files) that haven't been mentioned yet:

• CorsixTH: Theme Hospital.
• OpenMW: Morrowind
• OpenRA: Red Alert (and others)
• ScummVM: Various point&click adventure games (Monkey Island, Legend of Kyrandia, Loom,....)
• Return to the Roots: Settlers 2
• VCMI: Heroes of Might and Magic 3

Palapeli. It's such a great jigsaw puzzle game.

Some I don't see mentioned yet:

• Simon Tatham's Portable Puzzle Collection ported to pretty much everything.
• Nethack (and its variants), Dungeon Crawl Stone Soup and Brogue are great roguelikes.
• For boardgame fans the original Keldon AI for Race for the Galaxy is open source and works very well on Linux.
• Fish Fillets NG is one I have fond memories of from many years ago.
• The Ur-Quan Masters is Star Control 2, another classic.

https://trilarion.github.io/opensourcegames/games/top50.html

Keep in mind that this list contains both full games and engines for closed source games.

Prboom+ for the Doom fans in the room!

I have fond memories of Megaglest, an RTS similar to warcraft 3.

https://github.com/ppy/osu

I played a lot of FreeCiv and had a lot of fun with it. Not sure if it's still dev/maintained

Neverball seems far less known than the other ones, but it's really good and has tons of levels.

Extreme Tux Racer is a nice ski racing game but tux the penguin has some aerial maneuverability for long jumps.

Warzone 2100 is a nice RTS, especially fun with friends