This post was part of Wikipedia but seems to have vanished recently due to the Epic Games free games database being removed, a few services have opted to preserve the information and I figured meh why not so here it is, everything Games with Gold ever.
The original Xbox and 360 Games list can be found here, the Xbox One Games list here and videos where applicable for the releases here
Xbox 360 and Original Xbox Games
Players with active Xbox Live Gold memberships (excluding trial memberships and "Free Gold" weekends) may download the games during their respective availability periods. When downloaded, the game belongs to the user even if they subsequently drop their Xbox Live Gold membership.
Two titles are released a month, with the exception of June 2014 (which saw a third game released alongside the second to celebrate the one year anniversary of the program), April 2015 (which saw the release of four games, two in each half) and December 2015 (which saw a third game released alongside the second). The first game is free to download from the first of the month until the fifteenth, and then the second being available to download from the sixteenth until the end of the month.
Future Games with Gold releases for Xbox 360 are also made available for Xbox One through its backward compatibility system, which first started in November 2015.