Fiasco

No, you roll dice at the start and then take turns picking dice from that pool. You decide relationships with two other people, and for each of those you pick one of a Location, Need, or Object.

Then from there you work out who your characters are and start doing scenes. There's some die-rolling there, but pretty much only during two phases. The rest of the game is, mechanics-wise, about determining who gets how many dice (and what kind of dice those are). Although the main point of it is acting out scenes where things go horribly wrong.