Another popular RP genre in Bay12 are the Suggestion games, often also combined with RTD (Roll To Dodge), on which the players control a character or a series of characters and suggesting what they should do, with the most liked ideas/the ideas author prefers (More than one may be chosen) being the canon ones.
What about FATE...where the players and the GM build the game world its self fromn scratch...its got very loose rules.
I haven't seen rolls being used for that. I think one of those is going on in the Literature subforum right now. Those usually work best with some sort of artwork alongside them (which I cannot supply without eyes bleeding =P). Hmm... I don't know. As a GM I like to have control of the plot, even if it's just a framework to be filled out later. I feel that having the plot develop as the players make choices is more interesting than the players simply coming up with the plot themselves.
Rolls re often hidden, but they are there in most games. Some examples of rolls being public re in You re an evil entity (Or something like that).