While I've never played, I've known people who loved Amber Diceless Roleplaying - which is a strange RPG that has no dice or other means of determining odds in game mechanics. rather it uses stats on a character sheet compared to stats on a given monster/encounter.
Rite Publishing is running a Kickstarter to pay for art and stretch goals for Lords of Gossomer and Shadow, using the diceless rules. It looks like it's doing pretty good as a Kickstarter with only 38 days left. Link here...