From Bulbapedia, the community-driven Pokémon encyclopedia.
Pokémon Day Care (Japanese: 育て屋 Day Care) is a place for Pokémon Trainers to drop off their Pokémon to be raised in the care of other people, either the Day-Care Couple or just the Day-Care Man. Pokémon in Day Care gain one experience point per step the player takes.
In the main series, it is free to put a Pokémon into the Day Care, and costs 100 plus an additional 100 for each level gained to take a Pokémon out.
Many Trainers regard Day Cares as an inferior method of raising Pokémon for several reasons. Aside from the cost, which can rack up quickly for lower-level Pokémon (as they require less experience to gain a level than a higher-leveled one), Pokémon will not evolve while in Day Care, even if they meet the requirements to. The moves Pokémon learn while in Day Care are also based solely on level-up: if a Pokémon is raised to a level at which a new move would be learned, the topmost move in its current moveset will be deleted, and the new move will be placed at the bottom of the moveset. This may result in a Pokémon learning unwanted moves, while forgetting ones which were carefully selected for it.
Day Cares do have their uses, however. Because of the way in which Pokémon are leveled up, a player can leave a low-level Pokémon that he or she needs to evolve for the Pokédex in Day Care, journey around for a short while, and pick up the Pokémon, ready for evolution. Another prominent use, of course, is for breeding.
Aside from Day Cares in Orre and Kanto, which raise only one Pokémon at a time, all Day Cares can raise two Pokémon at once, and if the Pokémon are of opposite genders (or are with a Ditto) and in the same Egg Group, an Egg may be produced.
In Pokémon Colosseum, if a Shadow Pokémon is left at Day Care, it will gradually be purified, however, this is not possible in Pokémon XD, as Shadow Pokémon are no longer allowed to be raised in Day Care.
In Generations I and II, when a Pokémon is taken out of Day Care, its experience will lower to the minimum value for its current level. Thus, a Pokémon which is very near to a level-up can actually lose experience if it is taken out before it gains a level. This is no longer the case as of Generation III.
In Generation I, the Day-Care Man will not accept any Pokémon that knows an HM move.
In Unova, the Pokémon Day Care will only accept one Pokémon initially. Two Pokémon may be left after the player has received the Bicycle in Nimbasa City. This makes breeding Pokémon impossible until the player has obtained the first three Badges. In Pokémon Black 2 and White 2, the Pokémon Day Care isn't accessible until the player has defeated the Pokémon League, as Skyarrow Bridge is blocked off until the player has completed the game.
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Please feel free to edit this section to add missing information and complete it.
Reason: Missing Daycares. Also, the B2W2 one is slightly different on the inside from BW..
In the anime
Several Pokémon Day Cares have been shown in the anime, in all five main regions.
In the manga
In the Pokémon Adventures manga
The Day-Care Couple on Route 34 in Johto helped Gold, by letting him train on the Pokémon entrusted to them. This training helped Exbo evolve into Quilava, after which he perseveres harder and accumulates enough experience for Polibo to eventually evolve in Ecruteak City. They also taught him to battle without his billiards cue and goggles, as well as how to exploit type advantages.
At the end of Platinum chapter, Diamond, Pearl and Platinum were seen at the Solaceon Day Care with Manaphy and Phione. The Day-Care Couple from Johto also appears, telling the trio about a boy they once knew, having known to affect a Pokémon's personality before hatching.
In the Pokémon Gold & Silver: The Golden Boys manga
In Pokémon Gold & Silver: The Golden Boys, the Day-Care Couple are young, as opposed to the usual older couple. In Let's Use Fighting Type Pokémon!!, they invite Gold to a tournament run by the Day-Care Center, and in A Huge Mysterious Tree!!, they give him a Pokémon Egg.