When a Pokémon with Intimidate enters the battle, it lowers the Attack stat of all adjacent opponents by one stage.
Generation III
In Generations III and IV, Intimidate's activation message reads, "<Pokémon>'s Intimidate cuts <opponent>'s attack!"
Intimidate has no effect on Pokémon who are immune to Attack stat reductions, such as Pokémon with Clear Body, Hyper Cutter, or White Smoke. This Ability will not affect a target with a substitute.
Intimidate now also activates when a Pokémon gains the Ability, such as via Skill Swap or Mega Evolution.
Generations V to VII
In Generation V, the message changed to "<Opponent>'s Attack fell!"
In a Triple Battle, Intimidate does not affect non-adjacent Pokémon.
Intimidate does not affect Pokémon with the Full Metal Body Ability.
Wild Pokémon are more likely to call for help when facing a Pokémon with Intimidate. It shares this effect with Pressure and Unnerve.
If a Pokémon holding an Adrenaline Orb is affected by Intimidate, the item will be consumed and increase the holder's Speed by one stage.
Generation VIII onward
Intimidate no longer affects Pokémon with Oblivious, Own Tempo, Inner Focus, or Scrappy. Intimidate also now triggers Rattled. Intimidate raises the Attack stat of a Pokémon with Guard Dog by one stage, instead of lowering it.
Outside of battle
From Pokémon Emerald onwards, if a Pokémon with Intimidate is in the first place in the party (even if fainted), there is a 50% chance it will prevent a random wild encounter that would have occurred if the wild Pokémon would be at least 5 levels lower than the Pokémon with Intimidate. It shares this effect with Keen Eye.
Generation VIII onwards
Intimidate appears to have no effect outside of battle.