Serene Grace

Serene Grace doubles the chance of moves' secondary effects occurring - specifically stat changes, status ailments, or flinching. It also increases the chance of flinching due to the held items King's Rock and Razor Fang from 10% to 20% (however, note that those items do not affect moves that already have a flinch chance). Serene Grace does not affect status moves or the Pokémon's critical hit ratio.

Game descriptions

Ruby, Sapphire, FireRed, LeafGreen, Emerald:Promotes added effects.
Diamond, Pearl, Platinum, HeartGold, SoulSilver:Boosts the likelihood of added effects appearing.
Black, White, Black 2, White 2:Boosts the likelihood of added effects appearing.
X, Y, O.Ruby, A.Sapphire:Boosts the likelihood of additional effects occurring.
Sun, Moon, Ultra Sun, Ultra Moon:Boosts the likelihood of additional effects occurring when attacking.
Sword, Shield, B.Diamond, S.Pearl:Boosts the likelihood of additional effects occurring when attacking.
Scarlet, Violet:Raises the likelihood of additional effects occurring when the Pokémon uses its moves.