Star Wars: The Old Republic has a fairly broad assortment of mini-pets for avid fluff-junkies like me. I have a few real-life pets myself, and there's something about pet ownership that humanizes even the foulest Dark Lord of the Sith. While the vanity pets in SWTOR don't really "do" anything, they have their own stories which add to the stories of the characters who own them - just like real-life pets - and that gives them an intrinsic value.
My own personal favorites come from the lore of the films. Find out about the movie counterparts of My Top 5 Vanity Pets.