Follow Me is learned by 9 species by level and 9 by egg

Effect, in PokéAPI's words

“Redirects the target’s single-target effects to the user for this turn.”

Who learns it

17 species in all, 8 of 17 games shown

Scarlet and Violet: 13 species

Species	Method	Level
Maushold	Level up	1
Ogerpon	Level up	1
Sentret	Level up	19
Furret	Level up	21
Clefairy	Level up	36
Clefable	Egg
Electabuzz	Egg
Magmar	Egg
Elekid	Egg
Magby	Egg
Pachirisu	Egg
Electivire	Egg
Magmortar	Egg

Brilliant Diamond and Shining Pearl: 9 species

Species	Method	Level
Clefable	Level up	1
Togekiss	Level up	1
Sentret	Level up	19
Furret	Level up	21
Clefairy	Level up	36
Togepi	Level up	40
Togetic	Level up	40
Pachirisu	Egg
Riolu	Egg

Sword and Shield: 5 species

Species	Method	Level
Clefable	Level up	1
Togekiss	Level up	1
Clefairy	Level up	36
Togepi	Level up	40
Togetic	Level up	40

Ultra Sun and Ultra Moon: 7 species

Species	Method	Level
Clefairy	Level up	16
Sentret	Level up	19
Furret	Level up	21
Togepi	Level up	21
Togetic	Level up	21
Pachirisu	Egg
Riolu	Egg

Sun and Moon: 7 species

Species	Method	Level
Clefairy	Level up	16
Sentret	Level up	19
Furret	Level up	21
Togepi	Level up	21
Togetic	Level up	21
Pachirisu	Egg
Riolu	Egg

Omega Ruby and Alpha Sapphire: 7 species

Species	Method	Level
Clefairy	Level up	16
Sentret	Level up	19
Furret	Level up	21
Togepi	Level up	21
Togetic	Level up	21
Pachirisu	Egg
Riolu	Egg

X and Y: 7 species

Species	Method	Level
Clefairy	Level up	16
Sentret	Level up	19
Furret	Level up	21
Togepi	Level up	21
Togetic	Level up	21
Pachirisu	Egg
Riolu	Egg

Black 2 and White 2: 7 species

Species	Method	Level
Clefairy	Level up	16
Sentret	Level up	19
Furret	Level up	21
Togepi	Level up	21
Togetic	Level up	21
Pachirisu	Egg
Riolu	Egg