Vista

A procedural piracy game, you command a ship to sail the seven seas, either alone or with friends. Explore, do quests, fight pirates, or be one yourself!

Unturned is a free-to-play cross-platform action zombie survival game with crafting elements.

Strafe is a retro styled pixel art shooter in the Unity engine that purports to offer endless play with procedurally generated levels.

A turn-based fantasy RPG in the vein of Baldur's Gate featuring cooperative multiplayer as well as a single player campaign.

The collection is actually the first game in the AI War series, Fleet Command, and five expansions released between 2010 and 2013. The developer, Arcen Games, is working on a new entry in the series due out later this year, called The Last Federation. All feature competitive and cooperative play against human or AI players. It runs on Windows, Linux and Mac OSX, and supports cross-platform multiplayer.
Steam has just put up for sale the entire AI War Collection: six titles for less than five bucks!

This free, open-source empire-building game lets  you lead your tribe from the stone age to the space age. Now there's an HTML version playable in browsers, even on mobile devices! Features network and play-by-email options as well, and supports Windows, Linux and OSX with cross-platform play. Currently the OSX version is out of sync with the latest stable version (latest Mac version 2.3.0, latest stable for Win/Linux 2.3.5).

The successor to the Quake engine-based Nexuiz, Xonotic is a fast-paced multiplayer shooter, similar to Unreal Tournament or Quake 3 Arena. Features FFA and team play.

The latest iteration of Sid Meier's famous strategy game series doesn't get listed on most sites as being a cooperative game, but that's only because how most alliances are temporary. That certainly doesn't need to stop you from getting together online with a few friends to beat up on the AI (or try to) before turning on each other!

According to its sourceforge page, Triple A is "a free online turn based strategy game and board game engine, similar to such board games as Axis & Allies or Risk." While it doesn't appear to have a discrete cooperative play mode, these kinds of games usually feature the ability for players to create informal (and usually temporary) alliances among themselves, so I'm including it here. Thanks to a former IMG writer who tipped us off to this gem!

This squad-based first person shooter is a full release based on a Source engine mod; it runs on OSX and Windows and supports crossplatform multiplayer as well as competitive and cooperative maps.

Built from the ground up for cooperative play and supporting OSX, Linux, and Windows, Left 4 Dead 2 definitely belongs on this list. And for a short time during the holidays in 2013, Steam offers the game for free!

This heist game isn't quite GTA but it is a cooperative bonanza: it works on Windows, Linux and OSX and supports both network and local cooperative play as well as cross-platform multiplayer. PC gamer in specific called out its excellent cooperative play mode.
Plus, it's on sale on Steam right now!
In fact, I think Blackstar and I are going to try this out at some point. I may even have some extra codes if there's interest...

A mix of roguelike and classic hack and slash 2d dungeon crawling gameplay, Hammerwatch is the complete package that features single player, cooperative multiplayer online or on a LAN, as well as a level editor-- and it runs on Windows, OSX and Linux and allows for cross-platform play. 
Title is available both on GOG and Steam. Steam has a 4-player pack for $24, but GOG sells each individual copy for $4 right now, so that seems like a better deal.
DRM-free!

Released on Early Access in December 2013, this first person action adventure RPG  features cross-platform multiplayer on Windows, OSX and Linux. The game looks to be pretty early in development, but seems to be snaring enough people to invest the hours in playing it.

This Kickstarted game will be released "when it's ready" but next year is as good a year as any for this sci fi real time strategy game. 
About the game:

Colonize solar systems, smash entire worlds, and obliterate your foes in epic battles with multiple players and thousands of units. Planetary Annihilation takes real-time strategy to a planetary scale. Control rumbling, powerful tanks of war, massive bomber jets, and an assortment of subs, bots, orbital units, and battleships.

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