A lot of games have stories to them. And by “a lot of games” I mean “virtually every title nowadays”. Back in the day it used to be only RPGs that put much effort into storytelling within the game proper, but even the others still tried to sneak some story in through alternate pathways like the manual. If you read the manual to the original Metroid you’ll find all sorts of crazy backstory that could never have been known by simply playing the game (e.g. Samus is actually male).
This is particularly amazing because at the end of Metroid the game reveals that Samus is a woman. I guess they didn’t read the manual.
Nowadays I think standards have gone up a bit. Not to say that every game is Shakespeare, but, generally speaking, everyone who works on a game now can agree on the gender of the main character (the occasional JRPG notwithstanding). It may not sound like much but is actually a huge step, and incidentally also one Shakespeare had to go through what with the only-male-actors thing.
I digress. Stories are in games, and they are generally a significant part of the gameplay experience. Unfortunately, due to the requirement of also being a “game”, video games tend to lend themselves towards story conventions that often weaken the story. The majority of video games, from FPSs to turn based RPGs, derive their gameplay from violence. This in itself isn’t the end of the world but it has two major implications: the storylines in video games must be action oriented (there will be no Citizen Kane for us, unless it is a game about trashing a room), and that they tend to involve a lot of fight scenes, which also tends towards lots of impersonal conflicts.
The important thing is not to miss out on the fact that characters are what matter from a storytelling perspective, not the faceless horde of cannon-fodder. Sometimes you can mix the two by throwing a really badass villain that can keep coming up whenever a faceless horde appears (Darth Vader and the Storm Troopers) and develop some characters and story that way, but that path only goes so far. What is more important is to centralize the characters into the climaxes of the story, and not to allow the epic scenes to become impersonal as well. If the story us about the fate of the world hanging in the balance of an epic battle, then that is a great story for having a huge fight where your character can kill a lot of Storm Troopers or Orcs or whatever. But the odds are the player doesn’t really care about “the world” so much as a few of the characters in it.
Probably the greatest example I can think of is in Lunar: The Silver Star. The solution to the epic, large scale, video-game-sized problem was unified with a threat to the main characters. Luna, a major character throughout the game until she is abducted part way through, turned out to be the incarnation of this goddess that the big bad guys wanted to use to rule the entire… never mind, you get it. In reawakening this goddess aspect of herself her own personality was erased, or at least buried underneath another personality. She is now hostile towards Alex, the hero, and threatening him. She also is a threat to the world. The important thing is that the player can’t just kill her to make the problem go away because that would be killing Lunda, and somewhere in that soul Luna is in trouble. There’s a great moment where you approach her after killing the villain and she shoots lightning at you (great video game moment: she’ll actually kill you if you don’t do something to reawaken her memories of you). It’s awesome because you know you want to save the world, but you really want to save Luna too, both for her own sake and for Alex’s. It combines the best of the epic and the intimate to create an emotionally engaging moment, and it is a template for how to do things right.