The only tabletop RPG that I've played for more than two sessions in a row is D&D 3.5 and Pathfinder (which is basically D&D 3.5) - until recently. I've been playing Apocalypse World by indie game design genius D. Vincent Baker...and it has been really awesome.
It's one of the most popular games on the story-games forums - (beat only by one of Vincent Baker's other games) but when I first read the text I didn't see what was so special about it. Of course, that's why we prototype and playtest - it's nigh-impossible to tell just from looking at a ruleset whether it's fun or not.
Sure, part of the fun may be the GM and people I'm playing with. These kinds of games, by virtue of their strangeness, draw players that are really into this kind of thing. This isn't a game I could pull out on family game night and say "How about we play this?" - I had to go looking.
But part of the fun is that half of the book is rules for the GM; not guidelines, not advice, but rules. The section on GMing begins: "There are a million ways to GM games; Apocalypse World calls for one way in particular. This chapter is it. Follow these as rules. The whole rest of the game is built upon this." The rules are a contract between GM and players, a contract where the GM is promising to deliver certain kinds of fun ... it has rules like Ask Provocative Questions And Build On The Answers. Which means when I play Apocalypse World with anybody as the GM, I know the GM is going to ask me to contribute to the story and respect what I add (unless they're breaking the rules.)
At its core, Apocalypse World is a very simple game. To show you how much this is not a board or war game, there are no rules for how far you can move on a turn. A wargamer confronted with this would no doubt ask, "But how do I know if I can get to an enemy without being shot first?" It's all in the narration and the roll of the dice.
But then, on top of this simplicity is exceptions. Like Magic: The Gathering or Cosmic Encounter, different classes and powers build upon the simple rules. A lot of these exceptions are the staples we've come to know and love from roleplaying: take +1 if you're doing such-and-such; but a lot of them are narrative exceptions, they give you as a player the right to deeply affect the story.
For example, the "hard holder" class - the "hard holder" player is essentially responsible for creating the hold, the home base and village that all the characters spend a great deal of their time in. Unlike D&D where the village is usually just a place to get your next mission and buy equipment, most of our game has happened in the hold, like a western where everything happens in town. And the GM doesn't create it - the player does.
And that gives me my link to videogames. There are a few videogames where you, the player, create the setting for the stories you tell: in particular, I think of The Sims, Dwarf Fortress, and X-Com. I'm specifically not including games that come with level editors - it's the interweaving of creating and playing that's particularly interesting. You're constantly working on and changing your house in The Sims, in-between getting involved with the drama your Sims create; X-Com you work on your base between missions - what a treat when that base gets attacked.
So The Sims is within striking distance of the new breed of collaborative-story rpg's. In fact, take The Sims - put it in a post-apocalypse future - make weapons and ammunition fairly easily and readily available - take out bathroom issues - and you start to get close to Apocalypse World, the computer game.
But it still wouldn't create good stories as consistently and reliably as story games do. In Apocalypse World, you're constantly running out of things, and threats are constantly emerging and getting more serious until you take care of them. Hard choices continually emerge, like "I can't save everybody - who do I save?" and "Am I going to have to kill this guy?"
Why doesn't that happen in The Sims and Dwarf Fortress?
Again, The Sims seems like it's in striking distance. You have all these resources you have to juggle, and limited time. You're constantly making choices - often, it's "Do I watch TV or go to the bathroom?" but there's also "Do I further my career or improve my relationship with my children?" How come that last choice, the fundamental choice of so many movies and novels, career vs. family, doesn't feel like a story when you play it out in the Sims?
It feels more like a game of whack-a-mole. "Children are getting unhappy. Play with them. Ok, back to my career." Which is a lot like real life, come to think of it - but not much like a story, where you have to choose, right now, at this one moment: "Do you go steal the moon like you've always dreamed or do you go to your daughter's dance recital, the one you pinky-promised you'd go to?"
Finding those moments is something computers are still bad at...but I expect somebody's going to figure it out before I die...