Slain Monsters Rest in Peace is a special modifier seen on only a few select items. It prevents monsters from being resurrected, either by other monsters or the player character.
This effect can be both beneficial and detrimental, depending on circumstances. Enemies such as the Fallen Shaman or Greater Mummy are made much more vulnerable as they will no longer be able to bring their guardians back to life, however resurrection skills that require the presence of a corpse will also be rendered useless. This can be especially harmful to Necromancers, who depend on bodies for multiple skills.
Despite the extreme rarity of this effect on items, it is not particularly valuable, as shattering frozen enemies grants the same basic results and is much easier to accomplish than finding an item with the Slain Monsters Rest in Peace effect.
Slain Monsters Rest in Peace will prevent a monster from being able to be resurrected, but it will also destroy the effectiveness of player skills that require a corpse, such as Corpse Explosion or Find Potion. To take effect, the monster must be killed with physical or elemental damage, not magic damage, however the Paladin's Blessed Hammer does work.
The following is a list of all items with Slain Monsters Rest in Peace:
In Diablo III, with the introduction of a Critical Hit mechanic, the value of this attribute decreased. However, as a reference towards the original Diablo II property, a new attribute was added: Slain enemies rest in pieces, a pun often used in popular art (notable examples may be Star Wars or Duke Nukem).
This adds a Critical Hit-like destruction of enemy corpse to every attack. Note that on Torment difficulty, presence of resurrectors (like Fallen Shamans or Flesh Shamans) does not allow the corpses to be destroyed by any means other than Critical Hits. Also remember that monsters that explode on death (Accursed or Grotesques, to name a few) will still do so, there is no way to prevent their final attempt of revenge.
All Holy damage skills and skill runes destroy corpses of enemies they kill, effectively having this property as a free trait. The only classes utilizing this damage type are Crusader and Monk, though.
These effects only destroy corpses that monsters can use: secondary resource of Necromancers, the corpses only visible to them, remain intact. This includes the Necromancers' own attacks, so they don't leave themselves without fresh bodies with their own critical blows.