For German-speaking readers (or anyone with reasonable Google Translate-fu), System Matters has a worthy article about using questions to collaboratively build fantasy settings - you could generalise to other genres, of course.
I'm a firm believer in asking questions at the start of games, even when using an existing setting. In particular, I like to establish things like:
- What genre is the game aiming at? If I'm not familiar with the source material, I need some explanation - it doesn't mean I can't play, but I'll want more information. This is a relatively common issue because of my lack of TV knowledge.
- How supernatural is the setting? A lot of games we play feature some amount of supernatural stuff, but I like to establish how pervasive we expect that stuff to be. Even in fantasy settings, this can vary a lot. Is this the kind where magic replaces technology even to the extent of things you could do a lot more conveniently without magic? The kind where every village or suburb has a local mage, or magical businesses are commonplace? Is magic something everyone has, or just a few people? Can you learn it, or is it a gift, or an external force? What is magic, anyway? Alternatively, is this a setting where the supernatural intrudes onto normality? If so, is it widely-known and acknowledged (Ghostbusters), dealt with by a few dedicated heroes (Buffy), or hushed up by secret government organisations (so many things)? Perhaps most importantly, how much of the time are we expected to be looking for supernatural explanations and solutions?
- How serious a game is this? This is a big one because most of our games are non-serious, but there's a whole gamut of frivolity from slapstick nonsense (some of my Cthulhu games), via irreverent parody, through to a pretty straight game with some silly names and the odd media reference dropped in character (most of our D&D games).
- What is our characters' place in society, or relationship to important figures?