While the concept of hit points is typically associated with role-playing games, they are very common in other game genres, particularly adventure/dungeon-crawl games and collectible card games. Hit points are supposed to represent the amount of damage you can take before you die, but the abstraction is a poor one.
Let's look at D&D. There are 3 different standard game elements that affect hit points: class, level, and constitution.
Your class (or profession) determines the type of die used to roll for hit points. For example, wizards use a 4-sided die, thieves use a 6-sided die, and fighters use a 10-sided die. This represents how good each class is at fighting.
Your level (or experience) determines how many of those dice you roll, one additional die at each level. This represents your character getting better at fighting.
Your constitution is a measure of your physical endurance, giving you extra hit points per level. This represents how innately tough your body is.
Putting these into practice makes for some pretty comical results. A 10th-level wizard is as good at "taking damage" as a 4th-level fighter. A character with a high constitution (+4 hit points per level) gains enough additional hit points at 10th level (40) to equal a maxed-out 4th level fighter. An average 10th-level fighter (55 hit points, no constitution bonus) can stand still and take 16 successful average hits from a short sword before dying, while a 1st-level wizard would drop after a single blow. It requires more healing to bring a fighter to full hit points than it does a wizard. And why is it that class and level determine how good a character is at "taking damage", but have no effect at all on how easy they are to hit in the first place?
For 30 years, I've accepted all this knowing it was fundamentally silly.
In reality--or as close to reality as a fantasy world can get--any 2 humans, for example, are roughly equal in the amount of actual physical damage they can take. Having a more rugged body (constitution) would improve this, but would have minimal or no effect as you gain more experience. Being better at fighting should result in taking less damage in similar circumstances as long as you are able to use your abilities.
This last point is very important. A devastating blow against a wizard might be fatal, while only scratching a fighter. However, if both were just standing there, the same blow should have similar effects. In the case of most magic, your class should be negligible. Why should a fighter be hurt less than a thief by a fireball or a magic missile?
We've come to accept the classical hit point system, but would it really be that much harder to adopt something that makes a little more sense? I'm not proposing that the D&D system be revamped; TSR does that often enough as it is. I am suggesting that [board] game designers should consider new paradigms.
For example, the current system involves rolling a d20 to attack, adding any class, level, weapon, and feat modifiers. If you match or exceed the target's armor class, you hit. Then you roll the weapon's damage--which might be a d6 in the case of a short sword--and add any strength and weapon modifiers.
I think that the better the target is at fighting, the lower the chances of doing high damage. The current system relies on the lower probability of a hit, but uses the same damage system. If we build the damage into the roll, it almost comes out naturally. For example, if you exceed the target's armor class by 0/1/2/3/4/5/6/7/8, the base damage might be 1/1/1/2/2/3/4/5/6. This has the effect of decreasing the damage amount as well as the chance to hit as armor class increases. Of course, such a system would require each weapon to have its own table, but with modern role-playing, character sheets are already computerized and auto-filled-in. Such tables would also allow various weapons to have non-linear damages, such as my short sword table above.
Should a wizard in chain mail take damage identical to a fighter in chain mail? Of course not. Your class and level should affect your armor class. The abilities of a fighter to not be hit and to turn potentially nasty hits into minor ones is a skill that comes with the profession and experience. A 5th-level wizard in chain mail might have an AC of 15, while an equivalent 5th-level fighter might have an AC of, say, 20! Using the above short sword example, an attack roll of 21 would do 4 HP to the wizard and 1 HP to the fighter.
What if they are both just standing there? In this case their combat skill is not factored into their AC. They would both have an AC of 15, and would take equal damage from equal attacks. Other things could also affect AC: what weapon(s) you are using, the directions various enemies are attacking from (eg flanking), being slowed or stuck in something (eg mud, web, entanglement), using the environment for cover (eg doors, pillars).
And what about spell damage? In the current system, a character with more hit points is less affected. But if fire, for example, should affect all humans equally, then class and level should not be a factor, although some characters may have special protection and/or special abilities to avoid/resist it. A group of characters with different classes and levels that fails a saving throw against a fireball should all be equally hurt by it.
In summary, what I am suggesting in this D&D example is that all characters have approximately the same number of hit points, and that they do not go up in large increments with experience. Some people are frail and others are tough, but not enough to justify 4 HP versus 80 HP. I would perhaps start each character with 20 HP, and allow them to assign "slots" to make themselves tougher, both at creation time and as they gain experience. This should be a difficult choice, equivalent to increasing an ability score or gaining a feat, and should be 1 or 2 HP maximum (ie dedicating a large amount of time to working out or whatever). I would cap hit points at about 30. Of course, this would require changing the entire weapon and spell systems.
Think about how silly the current hit point system is, and dare to challenge it in your designs.