I recommend Heroquest. It's remarkably simple and open and it confers a great amount of narrative control on the player characters in exchange for minimal mechanical background, and allows you to solve problems with applications of your character's competencies.
As an example of how the system runs:
D&D: I have Dex 18, A BAB of +15 and 14 combat-related feats and a +3 weapon therefore I am an awesome swordsman.
Heroquest: I have a stat called "Awesome swordsman" rated at 13.
Your 'keywords' can be whatever you want, and you have abilities which are specially favoured under them. A character sheet might look like:
RARITY
Keyword: SPIRIT OF GENEROSITY 18
Charm +3
Whining +3
Keyword: FASHIONISTA 25
Dressmaking +4
It Is On +1
Style +2
Keyword: UNICORN 15
Precision Work +2
Finding Gemstones +4
It's us against the world, man. *Brohoof*