The problems that most Linux (or Open Source games) have are graphics and AI. Therefore, turn-based games tend to be the best because in those you can fiddle with both.
My favorite game for sure is
Battle For Wesnoth. It's turn-based strategy, not unlike the in the West relatively obscure Fire Emblem games. Its production values are so high, it could easily pass as a commercial game. Graphics, sound and usability are on a very high niveau. I spent countless hours playing this in multiplayer. I'd still play it if I had a proper opponent. There are also excellent solo campaigns and tons of user-generated content like extra campaigns, new factions, new modes like co-op survival or mods that change the gameplay to something else entirely.
[BIMG]http://www.wesnoth.org/images/sshots/wesnoth-1.4-8.jpg[/BIMG]
Link
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UFO Alien Invasion is, well, a clone of UFO: Enemy Unknown. If for some mysterious reason you do not know what the UFO series is about, it's quite simple: Aliens attack Earth, you attack aliens. During missions, you control your team from an isometric perspective and it plays pretty much like every other turn-based, tactical RPG. Between missions you research the alien corpses you produced, backwards engineer their technology, assemble your teams, get money and construct buildings. It's fun and addictive. The last time (about 1.5 years ago) I played UFO Alien Invasion it wasn't quite that far but it seems it made some decent progress while I was not looking.
[BIMG]http://ufoai.ninex.info/wiki/images/thumb/Ufoai2.2_grenade_launcher.jpg/800px-Ufoai2.2_grenade_launcher.jpg[/BIMG]
Link
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If you believe that
FreeCiv is a Civilization clone then congratulations, you are absolutely correct. More specifically, it's a replica of Civilization II. There isn't really much to say about it otherwise. You choose the fate of a single civilization from the dawn of human culture to modern times.
[BIMG]http://upload.wikimedia.org/wikipedia/commons/b/b3/Freeciv-2.1.0-beta3-sdl_slack11.0.png[/BIMG]
Link
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This is the story
of a girl whose heart was standing still
and a boy whose breath was being stolen away,
both of whom die.
This how
Narcissu inttroduces itself. It's a visual novel and therefore very different to the other games here. It's of Japanese origin and one of the only visual novels that got a Linux port. That was probably because it was already freeware when that happened. However, the story itself is quite touching and very well done if you ask me and if you have never played a visual novel before, I think this is a good place to start.
[BIMG]http://upload.wikimedia.org/wikipedia/en/9/96/Narcissu_english_Linux_title.png[/BIMG]
Link
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ScummVM is an open source software that allows one to play old adventure games like Monkey Island, King's Quest or The Legend Of Kyrandia on modern computers. It's pretty much an emulator but it naturally comes without games. However, there are two quite excellent available for free that are to be played with ScummVM. The first one is
Flight Of The Amazon Queen, which is an Indiana Jones pastiche, and
Beneath A Steel Sky, which is a cyberpunk story set in a dystopian future.
[BIMG]http://www.gamingonthecheap.com/wp-content/uploads/2008/04/fotaq_2.png[/BIMG]
[BIMG]http://ubuntu.allmyapps.com/data/b/e/beneath-a-steel-sky-beneath-a-steel-sky/UBUNTU-8.04/Beneath_a_steel-sky.png[/BIMG]
Link (for ScummVM and both games; scroll down for the games)
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Besides from that you can find clones of pretty much every arcade or puzzle game in existence. And if you are a Windows user and still interested in any of these games, yes, all of them are available for Windows and most likely also for Macs.