Great suggestions in this discussion! Rather than adding my favourites, I will add some resources that list more games.
Libregamewiki: it is really comprehensive (sometimes too much, including even not-so-good-games). They care about licencing and is is very easy to browse, top-notch for me.
Open source games: a more relaxed repository, with lots of material.
bobeff open source list: this is curated, which means that there are not so many games but each and every one is stable, good, maintained.
Arcane Cache: a fantastic blog with reviews of libre games — or more precisely, underground games, there is a lot of discussion on how gamedevving philosophy too. The reviews are always in-depth and allow you to experience the games on another level, and each game is a small jewel in its category. Strongly recommended!
Battle for Wesnoth is the one that comes to mind first. Turn based strategy game.
Dungeon Crawl Stone Soup classical roguelike, as in actually like Rogue/nethack. Can be played with ASCII or graphical tiles, and you can play in a browser window with scoreboards and a spectator mode.
Some of the most polished open source games are: 0 A. D., Xonotic, Beyond All Reason, Battle for Wesnoth, Mindustry, Minetest, Thrive. These are all great games open source or not. I'm sure I'm missing a few, but these stand out to me for their completeness and polish.
I wasn't expecting to find a new "polished" open source game I've never heard of from this thread, but somehow I've never heard of Thrive before. It's even got a steam release!
OpenTTD is more a strategic game,but it's great.
OpenRCT sadly requires the graphics of the original RCT2, so it's not really open source.
But also a favorite.
0AD is great. And whilst not a game really, FlightGear is the best you'll get for a FOSS flightsim. And really, for the prices that some X-Plane/MSFS planes and other addons go for, it's actually proper good.
Cataclysm: Dark Days Ahead, has a really strong community behind it. Be warned, it is an intensely deep simulation (as in dwarf fortress), that is often criticized for it's tediousness. But that gameplay element critique aside, it's a fantastic example of a community developped game.
Cataclysm: Dark Days Ahead, or if you like something a little less complex, Cataclysm: Bright Nights, are fantastic roguelike games. Proper traditional, turn based, tileset ones.
Imagine a mix of Fallout and The Walking Dead, that's what it's like. It's superb. The possibilities are endless
Warzone 2100 is an excellent RTS that is open source. I've never played a game with a bigger and more complex skill tree. Has an interesting development history in that it was originally a Playstation game, but was completely open sourced once the company went under. It has been kept alive by fans ever since.
Forge, a Magic: The Gathering rules engine available both for Windows and Android. Various formats, good AI, offline and online play, and now even has a Shandalar-like mode. #MTG#MagicTheGathering#Forge#Shandalar
I like re3, reVC and reLCS. These are reverse engineered versions of GTA 3, Vice City and Liberty City Stories with improvements. Take Two has thrown a strike on the main repository, but you can still find mirrors or builds in the internet.
Colobot was made open source a while ago and is still great! The game assets (and original binaries) can also be downloaded for free from the dev's site.