Ratskinner
Adventurer
All editions: dying and near-death mechanics. Before 5e there really aren't any - you're fully functional at 1 h.p. and dead (or unconscious) at 0. There's no in-between state where you're wounded but still sort-of able to function; this would really need some sort of wound-vitality system which D&D has so far resolutely refused to implement even though to do so would be very easy. 5e has death saves etc. but the implementation still has a host of problems.
Lanefan
QFT.
Even if the game just occasionally kicked out a "wounded" condition, that might help. (I suppose you could theoretically have Critical>Serious>Light wounds as well, for completeness' sake.)
It always seemed weird to me that a troll (or Regeneration in general) could "reattach a severed limb"...and yet there is nothing particular in the game that can severe a limb. Not a big deal for the troll, the GM can just narrate that in...but I dare you to narrate a PC getting a limb amputated before the party can regenerate it! (unless you let the Cure spells handle that...)
I've actually added my own little mechanic to 5e to replace the 0 HP mechanics:
If you reach 0HP or are hit while at 0HP, then roll 4 dice. Odds are good for you, evens are bad. Assign the results to the following questions:
1) Are you Dying? (Roll d6, you have that many rounds of life left.)
2) Are you Unconscious?
3) Have you lost something precious? (An Item, weapon, limb, eye?)
4) You or the GM, who narrates how this goes down?
Characters at 0 HP cannot make the Attack action or participate in any aggressive combat action. They are too frightened, injured, whatever-being-out-of-divine-favor-is to continue.
It really makes getting dropped an interesting moment of play, rather than just feeling left out as per normal D&D. I've been running a 5e game for about a year now, I've taken one character's ear, a two magic items, a suit of armor...and an axe, I think. Its surprisingly fun for everyone to watch them grapple with the choice of "Should I be Unconscious or Dying?" I can't tell you how many times we've watched the "conscious-but-dying" wizard run for cover with a sucking chest wound.