A Pokémon with Stench has a 10% chance of causing the opponent to flinch when hit by a damaging move (provided the ability-bearer strikes first as usual).
Stench does not stack with the items King's Rock or Razor Fang, so an ability-bearer holding either item will keep the flinch chance at 10%.
In Generations 3-4, Stench has no effect in battle.
If a Pokémon with Stench is the leading party Pokémon, wild Pokémon are only half as likely to appear.