Gluttony

A Pokémon with Gluttony will use a pinch berry when its HP drops to 50%, rather than the usual 25%.

Pinch berries are: Figy, Wiki, Mago, Aguav, Iapapa, Liechi, Ganlon, Salac, Petaya, Apicot, Lansat, Starf, Micle and Custap. (Their descriptions state that they work in a pinch.)

Game descriptions

Diamond
Pearl
Platinum
HeartGold
SoulSilver
Encourages the early use of a held Berry.
Black
White
Black 2
White 2
Encourages the early use of a held Berry.
X
Y
O.Ruby
A.Sapphire
Makes the Pokémon use a held Berry earlier than usual.
Sun
Moon
Ultra Sun
Ultra Moon
Makes the Pokémon eat a held Berry when its HP drops to half or less, which is sooner than usual.
Sword
Shield
B.Diamond
S.Pearl
Makes the Pokémon eat a held Berry when its HP drops to half or less, which is sooner than usual.

Other languages

EnglishGluttony
SpanishGula
ItalianVoracità
Japaneseくいしんぼう (Kuishinbō)
GermanVöllerei
FrenchGloutonnerie