3 species have Insomnia as a hidden ability, 14 as a normal one

Effect, in PokéAPI's words

“Prevents sleep.”

As a hidden ability

Species	Slot	Note
Delibird	Hidden	Since Generation V
Pumpkaboo	Hidden
Gourgeist	Hidden

As a normal ability

Species	Slot	Note
Drowzee	Normal
Hypno	Normal
Hoothoot	Normal
Noctowl	Normal
Spinarak	Normal
Ariados	Normal
Murkrow	Normal
Shuppet	Normal
Banette	Normal
Honchkrow	Normal
Tarountula	Normal
Spidops	Normal
Capsakid	Normal
Scovillain	Normal

Elsewhere in PokéAPI

7 more holders without a page here

Alternate forms and other species that PokéAPI lists with Insomnia.

Pumpkaboo Small (hidden), Pumpkaboo Large (hidden), Pumpkaboo Super (hidden), Gourgeist Small (hidden), Gourgeist Large (hidden), Gourgeist Super (hidden), Mewtwo Mega Y