It has always bothered me that once unconscious, characters in D&D die so quickly. A character brought to -1 hit points dies 9 rounds later at -10 if he doesn't stabilize, which means that a person that doesn't stabilize dies in less than a minute of injury. I feel that's unrealistic, given actual data on wounded people even before the marvels of modern medicine. Also, the toughest guy in the world dies just as fast as the 98-pound weakling once he's brought to -1, which I also think is absurd. So, I present this variant rule to replace the "Dying (-1 to -9 Hit Points)" section of the PH on page 129 (and any other mentions of dying at -10 hit points).
 

Variant Rule: Slower Dying

    When a character's hit points fall to -1 or below, he's dying.
    He immediately falls unconscious and can take no actions.
    At the end of each round (starting with the round in which the character dropped below 0), roll d% to see whether he stabilizes. He has a 10% chance to become stable. If he doesn't, he loses 1 hit point.
    If the character's negative hit points ever drop to his Constitution score or lower, he no longer has a chance to stabilize each round and automatically loses 1 hit point per round. For example, a character with a 10 Constitution brought to -10 hit points can no longer try to stabilize and automatically loses 1 hit point per round.
    If the character's negative hit points ever reach his Constitution score plus ten (or more), he's dead. For example, the Con 10 character dies automatically after reaching -20 hit points (Con 10 + 10) or lower.
    You can keep a dying character from losing any more hit points and make him stable with a successful Heal check (DC 15).
    If any sort of healing cures the dying character of even 1 point of damage, he stops losing hit points and becomes stable.
    Healing that raises the dying characterÌs hit points to 0 makes him conscious and disabled. Healing that raises his hit points to 1 or more makes him fully functional again, just as if heÌd never been reduced to 0 or less. A spellcaster retains the spellcasting capability she had before dropping below 0 hit points.

Yes, this means that characters are less likely to bleed to death after being injured. I think that's OK. This also means that it's not so easy to kill a character at 1 hp with one attack (definitely a problem at higher levels with monsters that routinely dish out more than 10 points of damage, and the PCs go straight from being alive to dead and rarely enter the "dying" state).. I think that's OK, too. So the dwarf with 20 Con is going to have 3 minutes of being dying before being dead, although 2/3 of that time he's still trying to stabilize. This also means that high-Con characters have more chances to stabilize. That's okay, too.