OK, my main problems with D&D are:
Hit Points &
Armor Class.
First, I want to explain that I think they are great at representing the abstract nature of combat. I think they are good are representing luck, exhaustion, and minor injuries. In fact, we still use them for exactly that!
The Problem:
However, I think they are terrible for representing serious hits / injuries / damage. To me this is obvious and I don't particularly feel the need to explain further. I will if asked.
The Solution:
The solution my group uses now was based on the 4e bloodied condition. We created a 2nd pool of hit points called bloodied hit points (BHP). BHP is based on size and fitness and doesn't grow as you level. It is basically fixed and low (1 - 10 max for Medium PC), and represent your PC's "meat." You take damage to BHP when your HP are 0 or on a critical hit (we used "confirmed" critical hits). This means a critical hit form a sword always has the potential to take you out, which feels correct to us. Additionally, BHP heal slowly. I BHP / week or you can use a healer's kit and a check to increase that to reduce that time. At 0 BHP you die.
In conjunction with BHP. we give all armor a damage reduction (DR) value = to the armor's AC -10. However, this damage reduction only comes into effect when your BHP has been hit. So, if you are at 9 HP and your hit or a critical hit, your armor reduces the damage of that hit before you subtract it from your BHP.
Example:
A fighter (9 BHP) in plate armor AC 18 (8 DR) is fighting a Huge Dragon. The fighter is at 0 HP and is hit by the dragon's claw for 15 damage. The damage is reduced by 8 (from the DR) and does 7 damage to the Fighter's DR. The fighter now has only 2 BHP and likely can't take another hit - he need to get the heck out of there.
Now, you could add all kinds of grittiness to this with lingering injuries and bleeding, but hat was to much for my group. For us, this system is fast, not very intrusive, and has the correct level of realism / game abstraction for us.
I'll check it out when I get home from work! I agree hit points are too abstract from my tastes, but I've yet to find an alternative I find elegant enough to replace them.