I would have the players write up something about what they want their character to be like. Personality, job, hobbies, family, whatever is important to them. These would be modern-day characters. Then I would give them back a fairly detailed character history. And that's all they would get. No character sheet. No knowing what's going on. No dice.
The characters would have different abilities and such, but they would be unknown (or mostly unknown) to both the characters and the players. They would have to discover what they can do and what's going on through game play.
This is a ways off, if it ever happens, since I would want to do a lot of prep work for it. However, is anyone theoretically interested in a role-playing game where you wouldn't ever see a character sheet or role any dice?