The Xbox Games with Gold program has been going strong for about two years thanks to its program that allows free games to be given out. It used to be that there was one free game, but now they have gone to two free ones. This is an update on Xbox Games with Gold Free Games for September and October 2015.
For the Xbox One, players have the option of getting The Deer God available until September 30th. According to the Steam Store, The Deer God is "a breathtaking 3D pixel art adventure that will challenge your religion and your platforming skills. It's a game about survival, reincarnation, and karma; all set in a breathtaking and unique 3D pixelized world".
A Definite crowd-pleaser for the Xbox One crowd is that Tomb Raider: Definitive Edition will be available as a free download from September 16th to October 15th. According to Amazon, this is the critically, acclaimed cinematic action-adventure, re-built specifically for next gen consoles. This will bring Lara Croft back to life in a lot of detail through many great adventures. It is good timing that the Tomb Raider: Definitive Edition is coming out with the soon to be released Rise of the Tomb Raider coming up.
From September 16th through the 30th, Xbox 360 users will be able to download Crysis 3. For those unfamiliar with Crysis, it is a first person shooter game series where the player runs around in a cool nanosuit fighting against aliens known as the Ceph. Crysis 3 is the final act of the series, and it takes place in post-apocalyptic New York City, as the player takes the Prophet to end the war with the Ceph once and for all.
I'll go ahead and answer the question that everyone is looking for as far as the free games for October 2015. The answer is sadly no answer, as the free Games with Gold are not usually announced until the month turns, and then there are usually only rumors. After doing several searches for October 2015 predictions Xbox Live Gold and similar keyword phrases, I could find no hint of any possible free game for October 2015. I suppose that I could probably start a rumor with a guess, but it really is anyone's guess. Maybe Xbox Live needs to have a Vote to Play like PlayStation.
I'll also answer the question about backwards compatibility, as it has been rumored that soon Xbox One users will have four free games to pick instead of the usual two. It hasn't been confirmed whether this will be the case. If it is, then that does change the playing field a bit.
There is currently no word about what is available in October 2015, but those games will be revealed towards the end of September.