I don't think it's relevant to what you're doing, but the most interesting way I have seen so far is in Amnesia: The Dark Descent (by the makers of Penumbra).
The basic principle of the game is that the character does not have any memory of what is going on, and you are alone in a castle that is alive - that is, something is chasing you, but you don't know what. You have to try to escape, whilst avoiding the monsters that will chase you around and stopping yourself literally going insane.
You cannot actually fight - one of the reasons its so scary (meeting a monster is certain death) - so there's less attributes, but you have 2: Health and Sanity. Instead of having '100/100 health', you simply get a description - 'A few minor cuts and bruises' or 'Struggling to walk'. And then low sanity made the screen go all weird.
I much preferred this over the standard 'you have 15/200 health left'.
An idea I was planning on using for my RPG:
Instead of a 'hit points', 'constitution', or 'strength' stat, you instead have 'upper body muscle' or 'arm dexterity'. It's very much a BODY PART + STAT system, but it makes more logical sense. I mean, if you worked out at a gym in a game running, then you would have much stronger legs, but having your hit points going up would be very generic - I have strong legs, so therefore getting hit in the chest doesn't do as much damage. In the same kind of way, a high strength would usually equate to a direct damage bonus. With a sledgehammer, this makes sense, but there's only a certain amount of power you can apply to a katana, say.
EDIT: I have remembered another stat system I was very fond of: Fallout 3.
It had your usual 'base stats' - strength, endurance, luck, perception, agility, intelligence etc. Then there were a number - I think about 23 - other stats. These stats actually defined your character more. For example, a high strength meant you could carry more equipment, but not necessarily meant you could do lots of damage with a baseball bat. In the same way having a high energy weapons meant you could do a lot of damage with a laser rifle, but wouldn't necessarily mean you were very agile.
Then each of the base skills had a trickledown of a few points to other skills - every point in strength gave about 1.5 points to melee weapons, for example. This made me as a player consider my stat choices much more than 'durrr shove it all in < weapon I'm using >'.