Hmm. Looking through a thesaurus a little, I came upon kismet and moira - the first meaning chance, and the other meaning circumstance. I think I like Kismet a little more. (On the other hand, jeopardy might be a good name too.)
On the one hand, we don't want kismet to result in bad things only happening to some folks - Everyone's playing the game, everyone takes the risks. The idea is that sometimes things go wrong, and they go wrong a little more often than the others. (I don't really want to muck around with gaining XP.)
So, if theives break into the adventurer's supplies and take things, then they're more likely to take something from Bob than Janice. If someone's family member is involved in the new plot, Janice's has been promoted to city council and needs your help cleaning out the sewer, whereas if Bob's family has to be involved, his kid sister has disappeared into the sewers and hasn't been seen. Bob tends to find the cursed artifacts, and Janice finds the useful ones. (Now, this shouldn't be an _always_ thing. Janice should occasionally discover that whoever wears the ring she's got on dies at the end of the month, and Bob should occasionally push his hand into a pile of dung and find the duchess' missing wedding ring.)
Think of it as a luck score. The higher your stats are, in general, the worse your luck - but with your stats, you should survive it. But it would allow someone to play a Jack - someone who's mostly pretty good in general, who keeps discovering himself tripping over some interesting bit of luck.
It's also an interesting guide to getting people to play with low stats. In point-buy, it's hard to end up with a sub-8 stat because that's the way the table goes. But if you expanded the table downwards (although not with as much of a curve as the positive does), it would give Bob a reason for his fighter to perhaps have a 5 INT and a 7 CHA - so that the kismet from his 18 STR, 18 CON, and 12 DEX wouldn't weigh too hard on his shoulders.
I would suggest that if a character faced some form of pernament ability drain, that his kismet be adjusted for that - if Bob faces something that lowers his CON to 14 pernamently, then that bit of bad luck burns off a little of his kismet.
Anyway, some more thoughts. Back to work.