This effect will occur if Natural Cure is the Pokémon's Ability in battle when it switches out and is not suppressed; a Pokémon that obtained the Ability with Trace will have its status condition cured when it switches out, whereas a Pokémon which has Natural Cure but has been affected by Gastro Acid will not.
Generation IV onward
Natural Cure also heals any status conditions upon completing a battle (if it was in battle at the end of the battle).
Outside of battle
From Generation IV onward, Natural Cure automatically heals status conditions upon the end of a battle.
In Pokémon UNITE, Natural Cure is Blissey's and Trevenant's Ability. Blissey's removes all status conditions from the user, but goes on a cooldown after being triggered.
Trevenant's causes the user to continuously recover HP for a short time after falling to low HP and it also reduces the cooldowns of the user's moves. When the HP recovery effect ends, this ability goes on a cooldown, but each time the user hits an opponent with any of its moves, this ability's cooldown gets decreased.
This Ability sometimes cures every bad status condition the Pokémon has.
In the anime
In The Power of Us, during two simultaneous disasters in Fula City, Toren and his fellow Scientists attempted to create an elixir out of Natural Cure in the Pokémon Research Pavilion. However, a blackout occurred before the solution could be finished, forcing Toren to improvise with Team Rocket's Lum Berries.
In the manga
Pokémon Adventures
Blissey
The Pokémon is healed from its status conditions upon switching out.
Marley's Land Forme Shaymin was revealed to have Natural Cure as its Ability.
Celebi is revealed to have Natural Cure as its Ability.
Trivia
In Pokémon Super Mystery Dungeon, Natural Cure is mistranslated as Natural Recovery, a direct translation of its Japanese name.
Due to the user interface displaying how many of the opponent's Pokémon have status conditions, even though Natural Cure does not have an activation message, it is possible to deduce that a Pokémon had Natural Cure the next time the Poké Balls representing the opponent's party are displayed.
In Generation III, this is when the opponent switches Pokémon.
In Generation IV, this is both when the opponent switches Pokémon and on the move selection screen.
From Generation V onward, it is visible on the move selection screen only.