Out and inside the dreamworld.
Updated to Generation 8:
Inkay and Malamar are currently the only Pokemon to have Contrary as a regular Ability. Shuckle, Spinda, Snivy, Servine, Serperior, Fomantis, and Lurantis all receive Contrary as their Hidden Ability.
Perversity is a Dream World-only ability. Only Shuckle, Spinda, and the Grass Snake family can inherit it.