Not "pets" in the sense that MMO players think of them (as little tamed monsters that run around and do your bidding), but, well, kind of.
A thought that regularly occurs to me when I think of my cat is that I have made a friend from a small, fanged, bizarre monster. Have you ever had a cat hiss at you? It's really scary- your fluffy, lazy, whining fuzzball turns into a spiky ball of fangs and horrible eyes. Holy shit, what is this fucking nonsense? I mean, she's even got weird powers- she can see in the dark, she's agile, she has multiple rending claws on the end of fairly nimble paws, she's got a mouth of nothing but tearing fangs...
But she's a sweet goofball. And a monster.
I think that the next game of D&D I play, I'm going to have some dude with a Displacer Beast or a Manticore or something, and they get along and you see some big ol buff guy wrestling with his monster that he's taken as a pet. Maybe it sounds silly, sure, so maybe they've domesticated a variety of some horrible monster and now they're not regular Manticores, but Manticats, and they're dog-sized manticores that are fantatically loyal and also kind of stupid.
That's all I've got, thank you and good night.