The ability holder is impervious to any moves that don't hit it super effectively. It does not affect status moves. It also doesn't prevent indirect damage like status effects, weather, recoil and entry hazards. Wonder Guard cannot be Skill Swapped or copied by Role Play but it can be Traced. Wonder Guard can be overwritten by Simple Beam, Worry Seed, Entrainment or Gastro Acid. Entrainment can also grant the ability to a target if used by one with this Ability.
Prior to Generation VI, if the Ability was hacked onto a Dark/Ghost type Pokémon, that Pokémon was impervious to all attacks except status moves and Struggle.
In Generation IV, Fire Fang and Future Sight could also hit due to a glitch with the former and the latter being typeless.