A Pokémon holding an Everstone cannot evolve by level-up or trade. (It does not prevent a Pokémon evolving via Evolution stone.)
From Generation IV onward, the Everstone fails to prevent Kadabra from evolving. If either Karrablast or Shelmet holds an Everstone when traded for the other, neither can evolve.
Breeding
Natures
This section is incomplete. Please feel free to edit this section to add missing information and complete it. Reason: Does the Everstone work if held by a female Pokémon bred with Ditto in E/DPPt? What happens if both parents hold an Everstone in HGSS/BW and in B2W2 onward?
If held by a Pokémon that has regional variants in the Pokémon Nursery, bred Pokémon will be the same regional variant as the parent regardless of the region they are bred in. (Normally, hatched Pokémon are always in the form corresponding to the region in which they were bred.)
In Pokémon: Magikarp Jump, the player carries an Everstone from start that keeps Magikarp from evolving into Gyarados. It cannot be thrown away but can be broken by tapping Magikarp repeatedly.