In 5e, most damage heals naturally over a long rest. Some monsters however have abilities or attacks that cause permanentlong-term harm, harm that is not cured by a long rest or by saving throws over time. Harm that requires magical restoration.
This makes these monsters potentially much more dangerous than their challenge rating suggests, if the magical restoration that is needed is unavailable to the player characters. It could leave the characters crippled for a long time. If the players know this, this can makes encounters with such monsters a stressful, high tension experience.
Which monsters in the Monster Manual can cause such effects?
(The question is about the Monster Manual to keep the list bounded and complete; if you do include monsters from other officially published sources, please indicate where they are from)
Qualifications
Death is Normal. Almost any monster can cause death by dealing normal damage leading to failed death saves. This may lead to permanent death in the early levels. If your character is level one, every monster is scary. But this would include nearly every monster in the book, and even at earliest levels, healing spells and stabilization are available to the players to make a single player death less likely, as long as someone in the party still stands and can help. So normal damage dealing or abilities that just reduce hp to 0 should not make you include the monster in the answer.
Permanent is relative. Nearly all harmful effects can be undone by powerful-enough magic. The question is about effects that do not go away by themselves. (Optionally, include examples of the lowest level abilities you know that could undo the effect, so the DM can see at which level the player characters could overcome it. This does not need to be comprehensive. Some monsters have effects that only trigger when nothing is done about earlier, less harmful effects. If you include guidance on how to end the effect, best include the answer to both stages.)
Damage is Normal. Almost any monster can cause death by dealing damage leading to failed death saves. If your character is level one, every monster is scary. But even at earliest levels, healing spells and stabilization are available to the players to prevent this, as long as someone in the party still stands and can help. So normal damage dealing is not sufficient to be included.
Long-term. Nearly all harmful effects can be undone by powerful-enough magic. The question is about effects that do not go away by themselves. (Optionally, include examples of the lowest level abilities that could undo the effect. Some monsters have secondary effects that only trigger when nothing is done about the first stage in time. If you include guidance on how to end the effect, best include the answer to both stages.)
I made the answer a Wiki, so you should be able to add to it and expand it.