Currently when creatures die, their bodies turn into a corpse, which is just an item. Items lack many of the abilities of creatures: they can't bleed, or get dismembered, or have an organized inventory, or be examined for distinguishing features, or decay bit by bit. In other words, corpses are much more boring and uninteractive than they should be.
So, corpses should act more like creatures. For combat purposes, they could act as a prone creature with really bad defensive rolls, although armor could protect the body even after death. You could keep hacking off limbs (useful if you need to bring back a head as proof, or if you're a sicko), and the corpse should keep bleeding until it's out of blood.
The detailed body info would also allow you to examine wounds after death, which would be helpful in cases of Sudden Dwarf Death Syndrome. Certain statuses like Drowning or Starving could also be preserved (changed to "Drowned," "Starved," etc. as appropriate).
Letting them keep their inventory (items they're wearing, i.e. clothes and armor, and also projectiles stuck in their body, but not held items) would make corpse hauling much more efficient -- dwarves could carry everything in a single trip, rather than hauling each individual sock. Corpses could also be properly weighed down by their armor (for purposes of buoyancy, etc.) If it were important, you'd also be able to determine what finger the corpse was wearing its ring on or whatever.
It's worth noting that many "corpse processing" actions, such as skin removal, should be doable on creatures whether they're dead or alive. Another point in favor of making corpses act like creatures.