I'm a big mythology fan, which is why it might sound weird that I don't really have a favorite beast or character. I find them all fascinating.
I like dragons, even when they're evil (see: Saint George and the Dragon); I like Egyptian myth for it's dark, earthy feel. Succubi and Incubi/vampires in general are always entertaining, as are werewolves.
One story that sticks with me though, despite the fact that I can no longer find mention of it, is this: Pavarti, wife of Shiva, sick of being made fun of for her dark skin, washed the darkness off of her in a sacred mountain stream. This darkness became incarnated as Kali, who is an aspect of the goddess Pavarti and wife to an answering aspect of Shiva.
She is associated with death, time, battlefields, and the feminine, though it be a violent, fighting feminine. She is the destruction-bringer, though if the destruction is yours or your enemies, is never clear, because she is an impartial goddess.
That's the first explanation I ever heard of her and it's stuck with me, true or not. Plus, there is definitely something to be said for a goddess who seems to be the complete opposite of the Greek goddesses, so consumed by their vanity and pride.
But of course it's been a while and I could be totally wrong.
Not gonna lie though, I totally have a thing for Loki (as in the trickster, thorn-in-the-side of Thor, bringer of Ragnarok) and Native American tricksters in general.
<3 the bad boys.