Some have a story "theme", some promote a story line through the levels/maps/incidents in the game. Multi-player is short on story, though it uses a theme.
Some, Like Halo, have a back story that comes out more strongly in the advertising trailers and and peripheral novels that they generate. The Halo: ODST trailers used live action to show the situation and back story of the game to great effect. The current Halo: Reach trailers do the same with animated live action. Each is a vignette which evokes a well spring of emotional response. Thus, they are telling a story, which the gamer is vicariously extending.
