It goes without saying that there is controversy as to weather games are actually works of art or flashing colors on a screen that rot away children's brains or make them act violently as my parents might think. While I would like to take the notion of one of these ideas and bin it to do so would be wrong because not all games express art or a story and not all games promote any sort of violence.
In my opinion for a game to tell a story while remaining a game and not just having a voice or text on the screen tell you whats going on every few minutes the story needs to be subtlety given to the player not just dumped on him all at once or crammed together into text boxes during loading screens. Its important to remember that the medium for telling the story is still a game where actions by the player need to affect the game world with restriction by the games rules.
Some people argue that the use of cut scenes allow for a game to share its story and while I agree that the proper use of cut scenes can help to convey the story to the player they can just as easily be misused.
So while games may have a few standard methods for presenting story to the player via character dialogues, cut scenes, or quest. Each of those methods can be used to present story to the player in a way that the player enjoys and doesn't subtract from his or her gaming experience or they can do just the opposite and drown the player in story and cover up the parts of the game that the player is supposed to interact with.
You don't have to punch me in the face with your story!
Again, in my opinion the best way to convey some complex narrative to the player is to have a good mix of scripted cut scenes, that blend well with the game play and tie well into what the player already knows from his or her active time playing the game and finding clues or completing quest or objectives that give him pieces of the story. Also giving pieces of the story to the player and letting them try to put the story together in their head or at the least having them thinking about events is another way to convey the story of the game.
Some games do this very well and I enjoy the experience more and then some games do it wrong by either cramming story down the players throat or filling the game with cut scenes(Asura's Wrath) or making me constantly press the a button to talk to my companion(Prince of Persia) to have them tell me whats going on. As a gamer and as a player I would rather be eased into things than have them dropped on me.