In battle
Generation III
When a Pokémon with Intimidate enters the battle, it lowers the Attack stat of all adjacent opponents by one stage
In Generations III and IV, Intimidate's activation message reads, "<Pokémon>'s Intimidate cuts <opponent>'s attack!" In Generation V, the message changed to "<Opponent>'s Attack fell!"
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.
Generation IV onward
Intimidate now also activates when a Pokémon gains the Ability, such as via Skill Swap or Mega Evolution.
In a Triple Battle, Intimidate does not affect non-adjacent Pokémon.
Outside of battle
From Pokémon Emerald onwards, if a Pokémon with Intimidate is leading the party, there is a 50% chance that a Pokémon that would be encountered will not appear if its level would be 5 levels or more below the leading Pokémon's. It shares this effect with Keen Eye.
Pokémon Mystery Dungeon series
In the Mystery Dungeon series, Pokémon attacking a Pokémon with this Ability with a physical attack will have a 20% attack penalty.