Never. There is no situation where a Pokemon would need a Neutral Nature. It's either Walling, Stalling, Attacking or annoying, so it needs either a Defensive nature for the first two, a Speed-raising / Attack-stat raising Nature for the third one and it needs either Defensive or Attack-raising Nature for the last. There is also FEAR, like you mentioned and also Riolu, with his Prankster + Copycat Roar combo that can utilize a neutral nature.
Source: Experience