Let's go for it!

Pine Marten

Cat

Snow Leopard

Golden Lion Tamarin

Arctic Hare

Alpine Chough

Snow Goose

Osprey

Caracal

Serpent

Crow

Terrier
And I don't recall there ever being a spider one- but if there was, it'd be pretty neat, right? You could keep it with you in your pocket and all!
Here's one that I think looks a little shy:

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She's Hyllus diardi, and they're actually the species that's considered to be one of the biggest jumping spiders in the world. The male and female ones look quite different, but they all have their own brand of sweet. Here's a picture of a tiny little baby, then one of a male following that.

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