The first free game awarded to Xbox Live Gold members is Defense Grid: The Awakening, which was released back in 2009.
According to Major Nelson, "I wanted to give you a heads up the next title will be Defense Grid: The Awakening. Normally 800 Microsoft Points, Defense Grid: The Awakening will be free for Xbox LIVE Gold members July 1st through July 15th ."
Defense Grid: The Awakening earned rave reviews for PC, Xbox Live Arcade and later PlayStation Network. The sequel, Defense Grid 2, will be PC in 2014.