In the core series games
Can be made into a Fast Ball by Kurt.
If used in the Apriblender, can produce a flavorless Aprijuice that has no effect.
In the anime
In the manga
A White Apricorn in Pokémon Adventures
In the Pokémon Adventures manga
In Yikes, It's Yanma!, an Apricorn lottery was used to randomly decide which pairs of Gym Leaders from Kanto and Johto would face each other in an interregional exhibition match at Indigo Plateau. Blue and Chuck got a White Apricorn each, pitting Blue against his former mentor.
In other languages