When the player kills a monster, sometimes it may leave one random item under its corpse it didn't already have when alive; these items are known as death drops. If a monster is neither a Kop nor a type which can't leave corpses, it has a 1/6 chance of leaving a random item on it.
Death drops can be left even if the corpse failed to generate, but any circumstances that explicitly prevent the monster from leaving a corpse (drawbridge, disintegration, digestion, undead on a graveyard level, and a few others) will prevent a death drop as well.
Death drops use the normal object generation mechanism, so the object class of the dropped item depends on which level the monster was killed in.  See Object#Item generation for a table of object class probabilities.
There is also a penalty against small monsters, who can only leave food rations, leashes, figurines, or items that weigh at most three. The game only tries to generate the item once; if it isn't eligible (as per above), no death drop is left.
Some monsters additionally always leave behind certain non-random body parts:
|dragon||dragon scales (1/3 chance, 1/20 if revived)|
|unicorn||unicorn horn (1/2 chance if revived)|
|long worm||worm tooth|
|iron golem||2d6 iron chains|
|glass golem||2d4 worthless pieces of glass|
|clay golem||49 + 1d20 (avg. 59.5) rocks|
|stone golem||statue of a stone golem|
|wood golem||2d4 quarterstaffs|
|leather golem||2d4 leather armors|
|gold golem||100-200 gold pieces (Luck-weighted)|
|paper golem||1d4 blank scrolls|
|gray ooze||a small glob|