There are more and more games that have world building as a part of set-up play. The group usually does this together, and the output is more and more focused on story, instead of building random events that create a life or setting. I'll start of with some examples.
The Blossoms Are Falling (Burning Wheel) has a few different "questionnaires" depending on the framework of the game the group is interested. Most, if not all, the questions also add game elements to character sheets, such as relationships.
In A Wicked Age has oracles which randomly determine seed ideas for the story at hand. It can be interpreted very loosely, but it's just concrete enough.
Diaspora uses random generation to determine some big variables, and each player takes on filling in the details. There isn't much direct story connect (IIRC) but I still count it because it's not one person doing the world building alone, and the act of doing as a group builds ownership. (In contrast to many games of the 80's or 90's where random tables seemed to be more about idea generation for the GM, without concrete ties to a group story).
What other games do this, and what do you think of how successful they are at getting a game started and helping to create interesting stories?