Like many people, I am not a big fan of having PCs be perfectly fine with 1 hp remaining and instantly dead when they are at 0 hp.
My approach to hit points is to not regard them as wound points but as stamina points. A succesful hit means that the target suffers minor scratches and bruises that interfere with its ability to succesfully deflect or dodge attacks and avoid serious injury. When a character runs out of hit points the extortion becomes too high and he slips, suffering a serious wound. It’s an abstraction like any way you can think of hit points, but I think it’s the best approach to have the fiction of the adventure match the rules of the game.
But the bigger challenge is how to handle the situation of a PC being reduced to 0 hp. I have a big dislike of the complex dice rolling and multiple modifiers of third edition and AD&D and I certainly don’t want to go through anything like the trouble of multiple successive rolls to stabilize and recover while having negative hit points. A much simpler approach is this:
When an attack deals more damage to a character than he has hit points left, the remaining points of damage are compared to his Constitution score. If the points of damage in excess of the current hit points is greater than the Constitution score, the character is dead. If not, the character is only unconscious for 10 minutes and permanently loses 2 points of Constitution. This loss of Constitution represents a lasting injury that neither surgery nor magic will ever fully reverse. While unconscious at 0 hp, any further damage will automatically kill the character. A character who regains consciousness is unable to fight or do other tiring activities until brought to 1 hp or more through resting or magic.
There are no saving throws or Constitution checks. Death and permanent injury are always automatic. In my past campaigns characters running out of hit points was always very rare already. Adding a significant chance to negate the effects only makes it even more unlikely that something bad will happen to a character. (Though running Sword & Sorcery dungeon crawls will probably increase casualties in my next campaign a lot.) I had considered to randomly determine whether the ability loss affects Strength, Dexterity, Constitution, or Intelligence, but with hit points already representing the ability to continue fighting I don’t think it’s necessary.
I like this solution since it’s both somewhat realistic in regard to actual battle injuries, and it also matches the habit of many Sword & Sorcery heroes to be left for dead with grievous wounds. As in Yojimbo or A Fistful of Dollars, being almost dead is nothing that a week of rest can’t heal, even if it leaves a lasting mark. With a Constitution score of 2d6+6, this gives a character about three to seven opportunities to cheat death before being too crippled to continue, though it might be worth considering retirement much earlier than that. It’s a lot more forgiving than the standard rules for death, but it’s still something that players really will want to avoid.