Stories are vital to nearly every game going. Although it could be debated that some genres do not require stories and would still deliver an enjoyable experience. Examples of this could be Tetris. You're not clearing blocks to save the princess or fight of aliens, you're doing it because it is your aim, plus it has a certain feeling of accomplishment when you slot that long block down the nicely placed gap that you created.
One great storytelling experience that I was sucked into (and have repeated 4 times now) is Final Fantasy IIV, and I have yet to play another game that has more depth or felling in it. There are so many things that make a good storytelling experience, but I think that one of the main things I look for is believability, because it is what makes the experience real and draws the player in.Stories in games are usually told by a character, NPC’s or a narrator. But in the world of MMORPGs, of which I am not very familiar with, the worlds are dominated by human controlled characters, and it’s these that create some of the most interesting stories. For example, when people wage war on each other, and I’m talking about hundreds of people invading a city populated by other ‘real’ people.
So I guess that a game can make a great story and not just be made by one.