For me, at least, the thing to remember is that there needs to be some kind of justification. Just saying "she has a dragon because she does, shut up" is a little weak (not that you would say that exactly). For example, my character went into Pythomancy [i]specifically[/i] to learn how to tame and care for a beast intelligent enough and intimidating enough to protect her from her many and varied paranoid phobias.

She sold out her services as a freelance medium, even when she was young, and finally, after years of searching, one of her contacts (a friend of the family) heard about someone selling the eggs of a Griffin. It had gone crazy and turned murderous, forcing the local knights to put it down. Since it's very rare to find such intact, living Griffin eggs, the Academy helped Ren (my character) to pay for one, on the condition that she would raise it at the Academy and allow its development to be studied by their Pythomancers.

By the time of the RP, it's about five years old and quite large, more than enough to make your average street toughs or vengeful clients think twice about taking advantage of her... So, she has a powerful Griffin companion, but he serves a very distinct purpose in her life, making her feel much more secure in herself among other people. I mean, at the very least it makes a better story than just doing it because it's cool.