I've been running some Numenera and Cypher System games here and there for people, and by far the biggest stumbling block for everyone has been hit points. In these systems you have three pools - Intellect, Might, and Speed. You use your pools to improve your ability to do stuff, but you also lose pool when you take damage. A common conundrum is: do you spend three speed pool to improve your chance to dodge an incoming attack that will deal eight might damage? If you fail, you'll lose a total of eleven pool - three from the spent speed pool, and eight from the sword in your belly. My first nigh-death at the table (PC was disabled but not quite dead from one hit) was a player who routinely was spending his pools down to be effective (yay) but hadn't thought about the effects that has on combat.
It is a very elegant system, in my opinion, but I'm the GM so my opinion matters little. Players are used to more traditional Hit Point systems which track wound levels as their own resource, rather than a resource that competes with potential skill rolls. Player happiness is useful, so I present alternative Hit Point rules for Numenera.
Each PC has a total hit point pool equal to the sum of their Might and Speed pools. All damage they take subtracts from this pool. When they are at or below half HP (round down), they are Impaired. When they reach 0 HP exactly, they become Debilitated.
Damage still has a type (speed, intellect, might), but instead of applying to their respective pools, they negate an equal number of edge points in that PCs stat for the next round of combat. So if you took three intellect damage from a Nano with Onslaught), you'd lose 3 HP and be unable to use up to 3 of your intellect edge for the next round. Overflow doesn't to extra damage, it just reduces your effective edge to zero. 1
If there is ever damage that would take them below 0 HP, the PC falls unconscious and must make an immediate death-avoidance roll. The difficulty of this roll is equal to the amount of damage they just took, and the avoidance type is the type of damage they just took (so if you were at zero and took three points of intellect damage, make a difficulty 3 test, target number 9). Note that in this situation, PCs will likely still have pool left, so they can use the normal effort rules (but remember the negated-edge rule for damage type) to improve their chances of survival.
Once a PC is unconscious (because they fell to 0 HP but did not die), they make a death-avoidance roll every subsequent round until they are stabilized by an ally. These rolls are might checks, and start at difficulty 1. The check difficulty increases by 1 for each round the PC is not stabilized.
A PC can be stabilized by an ally who makes an intellect check at a difficulty equal to the most recent standard death check (minimum 1 if the PC hadn't had a turn yet). This really should take more than a round, but this is a Role-Playing Game, so there we are.
So there you have it. These rules should end up being about as deadly as regular play (your total point buffer before death is lower, but you're less likely to deplete that buffer through non-combat actions). It also adds some "not quite dead yet" wiggle room at 0 HP, but doesn't go into negative HP (a feature I'm not fond of at all in GURPS and D&D).
For really lethal fights, allow edge to become negative in overflow situations - effectively raising the cost of effort for the next round. This has a secondary pool-depletion effect, but nicely models the shock and disorientation of being punched in the face. ↩