"Game" 64 first became popular when the Nintendo 64 was released. The system's flagship launch title, Super Mario 64, was the first to sport the moniker. The number was also used as a tentative title for games still in development. An example of this come from The Legend of Zelda: Ocarina of Time, as its development title was "Zelda 64".
Some games for Commodore 64 and Hyper Neo Geo 64 also used this naming structure. Games that are remakes of these titles, or are tributes to the era(s) they released in, may also have "64" in the title.