The Dead Land
Expanded from p. 273 of the DMG. Creatures sustain lingering injuries when they drop to 0 hit points. Injuries before that should be narrated as nicks and scrapes and flesh wounds: they're being battered a before a more direct attack sends them down. Injuries are separated by damage type, so use that to inform how you choose and describe exactly what horrible thing has happened.
If a character reaches 0 hit points after taking damage from a relatively minor effect, you may of course choose to ignore this rule. It would be a bit silly for somebody to have an arm ripped off by the bite of a small animal, for instance, though something like that might still be enough to cause damage.
Unless otherwise specified, the use of high-level magical healing, such as the heal spell, deals with any but the most extreme of these effects (lost limbs, eyes, and other bits would likely be harder to replace, requiring the use of a regenerate spell or something similar).
Acid and Fire Damage
1: Flesh and bone is burned away. You lose an arm or a hand. You can't hold anything with two hands, and can hold only a single object at a time.
2: Flesh and bone is burned away. You lose a leg or a foot. Your speed on foot is halved, and you must use a crutch or similar aid to get around. You have disadvantage on Dexterity checks made to balance.
3: An eye is burned out. You have disadvantage on Perception checks that rely on sight and on ranged attack rolls. You go blind if you don't got no eyes.
4-5: Your lungs are scorched by smoke and fumes. You have disadvantage on Athletics checks and on Constitution saving throws. With a reasonable amount of rest, you return to normal after a month.
6-9: Horrific scarring, with some parts of your face being completely eaten away. Most other creatures will not be immediately friendly to you, and you have disadvantage on Persuasion checks and on checks (usually Intelligence) to mask your identity by the use of a disguise kit. You do gain advantage on Intimidate checks, however.
10-12: Clothing and skin burns away. What skin you have remaining is covered in painful blisters, and deeper tissues are damaged as well. It will take at least a month to recover. Until then, rest and recovery takes you twice as long as usual, and your hit point maximum is reduced by 10.
13-16: Superficial burns. Pain and peeling skin with some scarring. Rest and recovery takes you twice as long until you finish a long rest, and your hit point maximum is reduced by 5 until then.
17-20: Minor scarring, blistering, bleaching, or darkening of patches of skin (depending on source of injury).
1: An arm or hand is permanently crippled, nearly ripped from your body by sheer force. You can't hold anything with two hands, and can hold only a single object at a time.
2: A foot or leg is permanently crippled, nearly ripped from your body by sheer force.Your speed on foot is halved, and you must use a crutch or similar aid to get around. You have disadvantage on Dexterity checks made to balance.
3: A crushing blow to the head makes it difficult to focus. You lose a point of Intelligence.
4-5: Your throat is crushed, preventing you from speaking until you finish a long rest. You struggle to breath, and for the next two weeks must make a Constitution saving throw every time you speak. On a failed save you take 1 point of damage, and cannot speak again until the end of your next turn.
6-8: Internal bleeding prevents you from spending hit dice or healing through rest until you complete a long rest during which you receive medical treatment or magical healing. You do not naturally recover hit points during that first long rest.
9-11: Your organs suffer a compression injury. Whenever you attempt an action in combat, you must make a DC 15 CON saving throw or lose that action and your reactions this turn. Requires treatment and a long rest to cure.
12-16: Minor internal injuries hamper you. Until you finish a long rest you have disadvantage on all Athletics and Acrobatics checks.
17-20: Your face swells up and your head is ringing, but you will recover with only minor scarring.
1-2: A limb freezes, dies, and falls from your body.
3-5: Toes and fingers freeze away, reducing your DEX by 1.
6-9: Your face is disfigured by frostbite. Disadvantage on persuasion and disguise, advantage on intimidate, NPCs are rarely friendly.
10-12: You are afflicted by a permanent chill, and heal half as quickly as usual.
13-16: Ulcers and intense pain. Whenever you are hit, you receive an additional 1d4 cold damage.
17-20: You escape without major injury.
1: The shock injures your heart beyond all but the most powerful magical healing. Whenever you begin dying, you automatically fail your first death save.
2-3: The arcing lightning burns away an eye.
4-5: A hand or foot is permanently crippled.
6-8: A shock wave deafens you for the next week.
9-11: The heat of the strike damages your lungs. You have disadvantage on all CON saving throws.
12-16: Superficial burns. It takes you twice as long to rest and heal until you next finish a long rest.
17-20: Minor scaring across your skin.
1-2: You lose an eye.
3-5: A hand or foot is permanently crippled.
6-8: Persistant internal bleeding. Whenever you are at less than full HP you lose 1d6 HP each hour. Can be healed if you complete a long rest during which another character performs a DC 20 medicine check on you.
9-12: A horrific internal injury hampers you. Whenever you attempt an action in combat you must succeed on a DC 15 CON saving throw or lose your action and all reactions this turn. Ten DC 20 medicine checks or high-level magical injury to repair.
12-16: You receive a festering wound, reducing your hit point maximum by 1 point each day until you receive magical healing. If this causes you to reach 0 hit points,
you die. Ten DC 15 medicine checks (max 1/day) will also heal the wound.
17-20: You receive a nasty scar, but are otherwise unharmed.
1-2: You are permanently blinded by intense magical light.
3-4: A hand or foot is burned away.
5-7: You are blinded until you finish a long rest.
8-12: Magical radiance weakens your defenses. You glow slightly, enough to be seen in the dark, and your AC is consequently reduced by 1.
13-16: You are singed, and are vulnerable to magical damage until you finish a long rest.
17-20: After a few seconds your vision clears. The attack spares you from major injury, sustaining only minor magical burns.
1-2: You lose an arm or leg.
3-4: You lose a hand or foot.
5-7: You develop a limp. Your speed on foot is reduced by 5 and you must make a DC 15 DEX saving throw each time you take the dash action or fall prone.
8-10: A deep cut leaves you winded and more vulnerable to further injury. You take critical hits when enemies roll a 19 or 20 against you and are vulnerable to slashing damage. A DC 20 medicine check made by another character while you are taking a long rest will heal you.
11-14: You are disfigured by a horrible scar. Disadvantage on persuasion checks, advantage on intimidation checks, not many NPCs are friendly.
1: You are rendered permanently deaf.
2-3: You suffer internal injuries from the sheer force of the sonic compression. Whenever you take an action in combat you must make a DC 15 CON saving throw or take 1d6 damage as cracked ribs and compressed organs protest.
4-5: You are deafened for the next week, and afterwards have disadvantage on perception checks that rely on hearing.
6-8: You are deafened for the next week.
9-11: You have disadvantage on all INT based checks until you finish a long rest.
12-15: You are deafened for one hour.
16-20: An occasional ringing in your ears is the worst you have to contend with.