I was recently discussing this topic with a few friends of mine, though in the context of whether it was possible to developing an MMO which was not about stat hounding but did provide extensive character development and a carrot to follow.
The development idea that we came up with was based around character development in feats, skills and rank with item customization by attributes. Basically: your character's only stats were Health and a 'Heat' bar (the more skills you used, the closer to full it became. Once it was full you could still use skills - it'd just start damaging your character too, to the point of permanent mutilation and death). You had feats, which were very broad abilities describing your character (think: athletic, bulky, sharp sighted) and had passive effects. For example, a skinny character would move faster but build up heat faster, where a fat character would move slower but build up heat slower. Some feats would open up a new line of items to equip or allow for a bigger skill set to be used.
Skills were your combat and non combat abilities. Think Fire magic, Fisticuffs (who doesn't like fisticuffs?), Gun shots, Lightning magic, you know, the cool stuff. Everyone could learn (actually learn, as in player experimentation) and use all skills, but you could only equip a certain number of skills; equipped skills wouldn't build up Heat, activate faster and be more powerful and usable.
Rank would have be our equivelant of levels, where you can see how much content a character has done. The more content you do, the better you do it, the higher your rank (think: sergeant, general, grunt, major, etc). Higher ranks would allow for more armor types, skill types, give you free bodyguards, make NPCs react differently, give you discounts, allow you to make custom missions, etc.
Of course you could gather and equip armors and weapons, but instead of having any absolute stats they'd be assigned an attribute. For example, common platemail has the attributes 'Heavy', 'Full cover' and 'Iron'. Heavy means it impairs movement speed. Full cover means it covers the entire body, increasing your health. Iron makes it weak to, say, lightning but resists physical attacks. In comparison, chainmail armor wouldn't be heavy or full cover, and only have iron as attribute. Cloth armor might have full cover, but have cloth as an attribute giving no resistances while being weak to fire. Stuff like that.
It was some pretty fun theory crafting to design a game which was in effect statless and classless. What does a system like this have to offer? It's easy and obvious while allowing for heavy customization. Why would it be better than plain numbers? It adds to the immersion of the player, which is very critical to the experience of any RPG.