WinXP

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.

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

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.

Out now on Steam on Early Access, Entropy is listed as a massively online action strategy RPG. Sounds a bit ambitious, no? And to boot, cross-platform multiplayer on Windows, OSX and Linux. (I'm wondering if the phrase "Unity Engine" is in there somewhere... it does look like the studio has used it in the past.)
Here's what the devs say:

A re-creation of the original Half-Life in the 2007 version of the Source engine, with upgraded high definition audio and video-- up until the Xen chapter, at least. There's no native OSX version, but if you install Steam into a WINE wrapper, you can use it to install the 2007 Source SDK and play it on OSX.

This classic sci fi shooter morphed into the multiplayer powerhouse Unreal Tournament, and supported Windows and Macs back in the day, but the processor and operating system transitions left the official Mac versions behind.
There are two ways to play on modern versions of OSX: One is a Cider version available at the Unrealism Zone; the other is a WINE wrapper available from The Porting Team.
Either allows the Windows game from GOG or Steam to be played on OSX, and cooperative mode is supported. 

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