Familiars/Animal Sidekicks

Abe Shuu wakes up 100 years after a catastrophic event and finds himself at level 50 of a "dungeon" type structure. He meets an adorable magical beast, a squirrel, named Tamiko, and they begin to level up together to reach the surface!

The sequel is here! Follow up to the manga Tensei Ouji wa Daraketai (also on the this list).

We have cave spiders, slimes, and a puppy! Hiel, our MC, is sent to an island (exiled) due to having an unknown "trash" crest. Turns out, the crest is the "Cave King" and he sets out to start turning this island into a home. He discovers not only can he mine, but he can also "tame" monsters, and so the stage is set!

Dude fails to die via Truck-kun and instead is electrocuted, opening up a cheat ability within a VR game he plays to make money. He quickly starts putting his new "ability" to the test and moves forward, gaining a mythical companion along the way, an adorable Fenrir puppy named Lucky!! (which means it goes on this list)

By the same author of Fairy Tail
Nightmares have flooded into the world. Some people team up with nightmares to get rid of dangerous nightmares, they're called nightwalkers.

Putting this here pre-emptively after seeing the anime for Ponta!!

So have some careful consideration, I've decided to add this to the list! The crows that each demon slayer gets (a sparrow for one) and the snake I think all qualify it to be here.
A young man's family is slaughtered and his sister is turned into a demon. In the hopes of turning her back into a human, Tanjiro sets out to become a demon slayer and kill the one who destroyed his family.

Kelvin is reincarnated into another world with no memories of his past life, he traded them for skill points. This is harem. Makes the list for Clotho (slime) and Alex (wolf).

A girl gets out of a barrier after 15 years and learns she possess a much feared and desired magic. A boy from her past appears and says he'll help her seal that power, but first we need to marry!
Makes the list because of Ainse a cat. Yes she does turn into a human form for like three chapters, so I'm making an exception.

Makes the list for Hamsuke, though probably pushing it.