The game doesnt need a key to be played. The key is only for logging into GFWL if you want to. (Though most people dont want to use that service anyway). The key should be located right below the disk in the case.
That's where I thought it should be located, much like New Vegas, but it's not. I want to use GFWL since I use it to track achievements since Fallout doesn't have any of their own. Has anyone else not had a CD-Key for the GOTY version?