Mystery Eggs

If there's a Pokémon that cannot be hatched, it's possible that it's a Recruitable Pokémon instead.

 are items that can be found in certain dungeons. These eggs hatch into Pokémon or unevolved forms of Pokémon that usually are encountered in the particular dungeon the egg was in. When hatched, these Pokémon know four random Egg Moves, unless the "Parent" Pokémon knows an egg move, in which case it will know that. Eggs must meet the following requirements in order to hatch; If the player has multiple eggs in their inventory, the steps taken will only be counted for the first egg in the inventory. So in order to hatch multiple eggs, the player will have to go through the steps required to hatch each egg one by one.
 * Eggs must be hatched outside of a dungeon.
 * The player must have an open slot in his or her party.
 * The player must take a certain amount of steps.
 * The steps required vary between species, and may also vary depending on the dungeon where the egg was found.
 * Using Pokémon with the Abilities Flame Body or Magma Armor will halve the steps required to hatch the egg. While taking the steps you must have the Pokémon with either of the aforementioned Abilities as your active Pokémon in order for the effect to trigger.
 * Having an Oval Charm held by any Pokémon on your team will reduce the steps required to hatch an egg by three times. It does not stack with Flame Body or Magma Armor.

Alternatively, eggs can be hatched at Joy, an NPC in all regions—and Tanren Undercity—for a fee. To use her service, you must have 1,000 Poké per egg in your bag. Using Joy's service will only incubate the eggs enough such that the player will require a few more steps (generally less than 10) to hatch them.

Trivia

 * Easter Holiday Caves are centered around hatching Pokémon eggs, and therefore have a couple aspects unique only to them:
 * At one point it was possible to hatch a level 1 Mightyena.
 * At one point it was possible to hatch escort Pokémon, resulting in the recruitment of Pokémon that are otherwise unobtainable with the Partner Egg system.
 * It is possible to hatch a level 1 Shedinja with the Partner Egg system.
 * Joy's service use to cost 5000 Poké per egg.