Vincent Baker has written a brief post on the level at which RPG play operates, and the level at which he thinks it ought to operate. If you're interested in making your game experience more about the fiction than the rules then you should at least read what he's written because in one way or another it will contribute to your RPG experience.
I take his point to mean that roleplaying should be about the story, and that events in the story should trigger game mechanisms or character sheet information rather than the other way around. Game rules should also immediately redirect the players back to the fiction in order to make events happen.
I think he has a valid point, but perhaps an incomplete one. There could be some interesting progress made on helping to identify characteristics of game rules which support this style of play so that game designers can create those kinds of rules.
Over to you, dear internet.