Just to add to the discussion, there's a diceless horror game called Dread that uses a jenga tower instead of dice. Actions cost pulls from the tower instead of rolls, and collapsing the tower tends to result in death (you can also punch the tower to sacrifice yourself heroically). It's heavily gm driven though.

Then there's also fiasco which still uses rolls for what results and events are but it is very heavily driven by roleplay. There are good dice and bad dice assigned based on the groups consensus of how an rp interaction went down. The thing that interests me about it though is that it's entirely GMless and could probably be modified to be diceless as well.

I feel like people can figure out diceless systems with some effort, but you need players who don't get defensive about their characters and are more interested in seeing the story play out than their characters succeeding.

(Both of these games were played on wil wheaton's tabletop on youtube btw.)