On occasion, I like to think about statting out various fictional characters in RPG-terms. One frustration I often have with this most geeky of passtimes is that, in most RPGs, a character's capabilities are well-defined across all areas. In fiction, this isn't the case. Unless it is a defining characteristic of a fictional character, you rarely know how strong that person is. Similarly, you might read a series of books centered around a particular character and not discover entire skill sets that the character has presumably always had until they become relevant to the story.
If I am playing, say, a Sorcerer in D&D who relies on blasting things with spells, my strength is probably wholly irrelevant. I might have an 8. I might have a 12. Is it really going to have a significant effect either way? Probably not. If it doesn't have an effect, why bother with it? Why not only record ability scores when they are notable? What would a system that took these considerations seriously look like?
Unknown Armies does this a bit - There are four stats (Body/Speed/Mind/Soul) and a few everyman-type skills, but beyond that all of a character's abilities are user-defined. This is pretty neat, even if it isn't exactly what I'm thinking of here.
I want to explore this a bit more. Let's use d20 as a framework. First, we'd get rid of the standard six ability scores. We'd keep the skill list, though. Instead of ability scores, we'd have some ability feats that you could take at character creation (and, perhaps, under special circumstances later). These might be things like "Great Strength: +2 to attack/damage and (some subset of) skill rolls" or - even more specifically - "Great Leg Strength: +2 to attack/damage on kick attacks, +4 to Jump rolls, and +5' base movement." Similarly, you could take Flaws such as "Weakling" or "Poor Eyesight" or whatever that would probably look a bit like the flaws in Unearthed Arcana.