Intimidate is an ability introduced in Generation 3. So far, 7 Pokémon have this ability.
Intimidate lowers the opponent's Attack stat by one stage upon entering the field. (unless it has Clear Body or Hyper Cutter) It affects both opponents in a Double Battle.
Outside of battle
If a Pokémon with Intimidate is the leading party Pokémon(even if fainted), wild Pokémon that are 5 or more levels below your Pokémon, are 50% less likely to appear. It shares this effect with Keen Eye.
Pokémon with Intimidate