Doom 3
Doom 3 is a science fiction horror video game developed by id Software and published by Activision.
Patches
Official
Unofficial but highly recommended
Parallax Mod Adds more depth to textures
OpenCoop - Coop the game online or on LAN with your buddies! Play the entire campaign start to finish, including expanchion pack. And extra challenge maps.
Mods
The Dark Mod
According to the creator's website, "The Dark Mod is a total conversion for Doom 3, turning it into a dark and moody stealth game inspired by the Thief series."
Open Source Version
The source code to the engine was released under the GPL license in November 2011. There have since been several modifications. You can view the different branches and changes, as well as download them, from the github repository, if you are willing to compile the code yourself. The same group that worked on ioQuake3 has said they will add features to the code and release compiled binaries under the title ioDoom3. You will have to obtain the art assets separately.