First off:
I'm guessing you haven't played Cataclysm or even Wrath then. Your questing in WoW now adversely affects the entire world around you. Towns spring up in places you libereated, creatures are defeated and the area around it springs with new life/spawns, you progress a storyline with characters who have purpose and help them reach their goals past just returning to them for a reward.
I haven't and that's pretty cool/step in the right direction. Darkfall was trying for something like that as well but from what I understand it didn't turn out well.
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Anyways, really I was just talking about player created story vs built in story. EvE does have that (somewhat), but the ones that came to my mind were:
Dungeon Crawl Stone Soup - There is no story whatsoever in the game, but when you die your character is deleted. This leads to really intense/high consequence games, which in turn leads to really fascinating stories on userboards from players about what their dudes went through. To this day I still remember a Minatour character I had.
Dwarf Fortress - Another zero built in story game, but the way a game evolves over time (as well as the intense detail and the inability to recover losses) leads to REALLY cool stories of games played (there's a whole subforum for them on the Bay12 games website.)
Jagged Alliance - I don't have the imagination for this but my brother invents the most amazing stories for his teams.
I've always felt that art imitates life to a degree, and the most interesting stories you can get are the ones that involve the dynamic reactions of humans to a dynamic world (aka "you couldn't make this shit up if you tried.") For that reason a player made story will always be more fascinating to me than a built in story (consider a good D&D game vs a game of Baldur's gate, awesome as it is.)
Moreover, when you are creating the story in this dynamic/human way, you do so through your character, or more truly, your avatar. You become more attached to it as you interact through it, as opposed to watching a movie through its eyes.
It's true that that's one of the reasons I like EvE, but really it's why I love ANY game (so to be clear this really isn't about pimping EvE). Give me a true virtual world. Give me a true interactive experience. I can watch a movie without a laptop. I can read a book on a desert island. What I want is the possibilities hinted at in otherland, neuromancer, snowcrash, or Ender's adventure with the Giant's Drink. I want the chance to really FEEL like a warrior exploring a strange, and yes, scary world. I want to feel amazement at the world. I want to feel sorrow at my losses. I want to feel pride in my achievements. I want to feel fear in the threats presented to me. I want to feel shame for my ignobility. I want to laugh I want to cry I want to hold I want to touch I want to be touched I want to .....
ok I am really sorry for this post. Anyways I just like player created stories better and I think that's the real future of MMOs.
Edit: Just to be clear though for single player games I do still LOVE story driven games, because they can be devoted to a single player they can become much more immersive.