Here's a long list of open-source video games.
Things that I have enjoyed and played a lot (which tends to weight towards heavy replayability, and place little emphasis on graphical appearance, story, or even on approachability to new players):
- Battle for Wesnoth. A hex wargame with nice sprite art. Think Battle Isle, Advance Wars, Panzer General...but with characters that gain substantial stats and abilities and a fantasy story. Lots of scenarios made for it.
- Dungeon Crawl Stone Soup. This depends greatly on whether you like roguelikes or not (see /r/roguelikes for people who do). These are games that are typically turn-based, often played on a text terminal, played on a square grid, with some character cruising through a dungeon, finding items and powering up and learning that a "Red Potion" in this life is a potion of healing. DCSS is probably the best-balanced of these, and has some helpful automation to eliminate grinding.
- Lincity-NG. This is a Sim-City like game, though the mechanics are very different. Graphics roughly Sim City 3000ish.
- Urban Terror. Not open-source, but free (and runs on an open-source ioquake engine). There are far-newer FPSes out there; this is from the Quake 3 Arena timeframe, but I still haven't found something that replaces it; it's much-slower-moving than a lot of the newer FPSes. Open-source FPSes that are much newer than this that might have more appeal include Xonotic (aka Nexuiz) and Warsow. Neither is comparable in terms of bling to current-generation commercial FPSes, though.
- Aisleriot, the GNOME solitaire game. Never thought I'd play solitaire much, but I've enjoyed it; it's an easy drop-in, drop-out game. Eight-Off is a great solitaire game.
- ET: Legacy, a community-maintained version of Wolfenstein: Enemy Territory.
Generally-speaking, in terms of genre support, running through Wikipedia's list of video game genres:
- Ball-and-paddle. Reasonably-well-covered though the flashiest ones I've seen tend to be commercial. I guess I'd suggest Lbreakout2; been around a while, though, and not 3D.
- Beat-em-up: No great coverage here. Honestly, I haven't seen much here by way of commercial games either recently; these were big in the arcade and so-so on home consoles in the late '80s and early '90s. There are some games here, but I haven't played them.
- Fighting games: No great coverage here (not even great commercial coverage, though I understand that the non-free Skullgirls is on its way in). There's also M.U.G.E.N., a generic fighting engine that doesn't look all that impressive to me (and which mostly seems to have mods disappointingly using content ripped from commercial games).
- Pinball: Nothing great and free (not even much non-free material). The incomplete and rather-limited Emilia Pinball is probably the best available here.
- Platform games: Abuse would probably be my top open-source and free recommendation (was once closed, and was open-sourced).
- First person shooter: I listed Xonotic and Warsaw above; I prefer the slower-paced but elderly Urban Terror, which is not open-source but is free.
- Shmup: Chromium B.S.U. is a bit long-in-the-tooth and simple, but open-source. Tyrian is an ancient PC-style DOS-era shoot-em-up that you might like.
- Rail shooter: I can't recommend anything here.
- Third-person shooter: I can't recommend anything here.
- Graphical adventure: Flight of the Amazon Queen is an elderly graphical adventure that was re-released under a free license, one of the family of games for SCUMMVM, the classic Lucasarts games.
- Text adventure: Here, Linux free gaming has very good support. You might want to grab something like Gargoyle if you want a pretty GUI client. Good TADS (Tads) and Z-Machine (Frotz) support is available. ADRIFT support (a rather more-limited environment) is available in the form of SCARE. You can find a vast library of very good games at IFDB or IFWiki. I personally enjoy Babel (one of the older games), but both IFWiki and IFDB have good recommendations schemes and lists of similar games. There is also a substantial adult interactive fiction game library, if that's of interest.
- Visual novels. Yes, a popular engine is Ren'Py, where games often look something more like the Japanese dating-sim games, with a fixed background, sprite-based characters superimposed, and a menu of actions to perform. There's a library of Ren'Py games available, and popularity-based recommendations with capsule summaries that would do better at recommending choices to you than anything I could do.
- RPGs. Relatively-limited, if you're not counting roguelikes. I have not played FreedroidRPG, but it's probably your best bet. I understand that FLARE, the Fallout/Fallout 2 engine clone, has some game content developed for it, but I haven't played it.
- Action RPGs. I can't strongly recommend anything here (this would be games like the classic Zelda or Secret of Mana series). Egoboo might fit.
- MMORPGs. There are various free-to-play games with Linux support. There are some options here that include free-to-play options. There have been lots of open-source projects that have gone essentially nowhere; WorldForge has probably gotten the furthest of these.
- Roguelikes. First-rate support; probably better support than any other platform out there. I'd recommend Dungeon Crawl Stone Soup, but tastes vary a lot here, and you may prefer something with fancier items and abilities (ToME 2) or the like.
- Tactical Role-Playing. Yes! Battle for Wesnoth could easily have been sold as a commercial game a few years back. The only downside is that there's a significant element of luck and keeping people alive can be important (like Homeworld, I found myself reloading to keep the best characters around for when I needed them). The game has steadily been more-fine-tuned over the years and had the content quality get better. This is a polished work. UFO: Alien Invasion is a good (albeit not finished last time I played it, years ago) X-COM-alike based on the Quake 2 engine. It didn't have the destructible terrain of the non-Linux, commercial Silent Storm, but other than that looked something similar.
- Construction and management simulations: I would recommend Lincity-NG. OpenTTD is a reimplementation and extension of Transport Tycoon Deluxe, and Simutrans another transport sim game.
- Life Simulation. Can't recommend anything here.
- Vehicle Simulation. FlightGear is the big open-source Linux civilian (non-combat) flight sim. It's a little more-oriented at hardcore civilian flight simmers than I am. There are actually some fairly flashy racing games for Linux, though I have not really played them: vDrift, TORCS, and Speed Dreams are all options.
- 4X: I can't recommend anything here.
- Artillery: Scorched Earth would be a 3d option. Atanks and xscorch would be 2d options. Hedgewars is like Worms.
- RTS: Most things here do not feel very polished to me or complete compared to commercial implementations. There's Spring, which is probably your best bet; it's got games comparable to a much-fancied-up Total Annihilation but AFAIK none with single-player campaigns. MegaGlest is another option, or 0 A.D.. I usually play RTS for the single-player game, and neither has much by way of a single-player campaign.
- Real time tactics: Nothing free and recommendable that I can think of. (Which is too bad, because I really like this genre; the Close Combat series is much-loved.)
- Tower defense: There are the same free-to-play-but-we-mine-data-about-you Flash games that exist for Windows; Gemcraft is a popular option. There are some interesting non-free options for Linux here, but not free stuff that I can think of.
- Turn-based strategy: Freeciv is probably the premier game here, rather like Civilization II. Also try Freecol. The elderly closed-source-but-free Conquest of Elysium is probably your best free Linux bet here. If you're willing to spend money, I would wholeheartedly recommend the other commercial games from Illwinter: Conquest of Elysium 3 and Dominions 3, which are very good turn-based strategy games; not graphically flashy, but have a very deep strategy game.
- Wargame: I never really got into these, but try Crimson Fields, or Advanced Strategic Command.
- Music: Frets on Fire
- Party Game: Can't recommend anything here other than the above Frets.
- Programming Game: There are probably more modern entrants; Crobots and Core Wars both work.
- Puzzle game: Pingus is a Lemmings clone. You might also try Trackballs, which I played a bit. There are numerous not-flashy entries in most distros; try running
apt-cache search puzzleon an Ubuntu or Debian system.
- Sports game: I'm not very familiar with the genre.
- Trivia game: I can't recommend anything here.
- Board game: See Pioneers.
- Trading card game: Blue Moon AI is an AI plus the content from the Blue Moon game. I find it to be a very difficult opponent; it's probably the best thing going if you like trading card games. There's also the same free-to-play Flash games that are available for other platforms, like Spectromancer: no monetary charge, but they're going to show ads and mine data.
List of free games on Desura
Top 100 free Linux games