5 species have Oblivious as a hidden ability, 20 as a normal one

Effect, in PokéAPI's words

“Prevents infatuation and protects against Captivate.”

As a hidden ability

Species	Slot	Note
Spheal	Hidden	Since Generation V
Sealeo	Hidden	Since Generation V
Walrein	Hidden	Since Generation V
Salandit	Hidden
Salazzle	Hidden

As a normal ability

Species	Slot	Note
Slowpoke	Normal
Slowbro	Normal
Lickitung	Normal
Jynx	Normal
Slowking	Normal
Swinub	Normal
Piloswine	Normal
Smoochum	Normal
Illumise	Normal
Wailmer	Normal
Wailord	Normal
Numel	Normal
Barboach	Normal
Whiscash	Normal
Feebas	Normal
Lickilicky	Normal
Mamoswine	Normal
Bounsweet	Normal
Steenee	Normal
Dondozo	Normal

Elsewhere in PokéAPI

1 more holder without a page here

Alternate forms and other species that PokéAPI lists with Oblivious.

Salazzle Totem (hidden)