My good buddy Boomer just posted a blog about his dislike of hitpoints. It's a great post. Go read it, then come back here and let me tell you why I like hit points.
One of the points my friend brings up is how RPGs often disintegrate into numbers, spreadsheets, and...perish the thought...a game. This is actually one reason why I like hit points. I have always believed that a good RPG is all three letters: The "RP" and the "G." One of the most common aspects of many games is the concept of resource management. Whether it's your pawns in a game of chess, mana in a game of Magic: The Gathering, or sheep in Settlers of Catan, a hallmark of great gaming is having a finite amount of Something with which you must manage successfully to achieve your goal (even if the goal is as lofty as "have fun.") One of the most fluid and vital resources that need to be managed in a good RPG is the player character's own life, his or her capability to continue to contribute to the game as it unfolds. To represent this as a dwindling pile of points is as straightforward and simple as it can get, and to date, I have not seen a better method. I agree with my buddy that the countdown clock introduced in Apocalypse World is a great alternative, but you strip away the flavor and it itself just boils down to little more than a small pile of hitpoints.
The real problem, I think...the thing that makes hit points so despised by those who despise them...is that there really is no better way around them. There are workable alternatives, like the ones Boomer described in his blog post. But if you care at all about that "G" in "RPG," then you need some kind of Thing to manage, and the most logical candidate for that Thing is your PC's health, and the most logical way to monitor it is as a number of points that increase and decrease throughout play.
But I sympathize with Boomer and every other gamer who are anti-hit points. I have three suggestions, to him and anybody else struggling to narratively handle them:
1. Let the GM be the sole tracker of hit points. Keep your players' HP totals yourself. Do not ever give the players the exact numbers. This forces them to pay attention to your descriptions. This also has the bonus of adding a little tension to darker or more intense games as the players will always be wondering how much more punishment they can take. The downside to this technique, of course, is that it places more pressure on the GM; not only is it one more number the GM has to keep track of, but now there is narrative pressure on the GM to make sure that every wound is described in exacting detail, so that a 10-point axe hacking doesn't sound like a 2-point scratch.
2. Use hitpoints as shields. Hit points don't just have to mean a characters' physical condition; hit points can mean any and all potential assets a PC may have to avoid taking critical damage. This means that when a PC loses hitpoints, it's not necessarily damage; it's just one more resource taken away. For example, a halfing rogue gets hit for five points of damage. The GM describes the nimble rogue darting behind a nearby statue for cover, the orc's trailing axe hitting the marble and shattering the statue into a thousand pieces. No physical damage is actually taken, but that rogue is now one step closer to death, as his cover is now gone. If you read closely the explanation of hit points in various editions of D&D, this is actually how hit points are supposed to work. It wasn't until those damned video game RPGs came out that hit points begun getting this rap as just someone's physical capacity to take punishment. Think of hit points as money you use to bribe Death into letting you survive a bit longer.
3. Play the right game. If you're absolutely done with hit points but do not want to larp it up, then select an RPG where lethality is a choice rather than a consequence. Cortex Plus and Fate Core are two great examples of what I'm talking about. Both of those games barely even mention death in their corebooks: everything there is framed as "being taken out," which can mean anything from being too nervous to move to hovering at death's door. Interestingly, Apocalypse Engine games aren't very good at this. Personally I think it's because the emphasis on Apocalypse Engine games isn't story; it's the conversation amongst GM and players about a fictional world with fictional characters. There's a slight difference, so slight it barely matters, but the one place it does is hit points.