I have a BUNCH of pets (so it's kind of hard to watch them all). I have noticed that they each do their own version of different dances.
The Wildclaw does the Michael J. Fox dance that is done at the prom in Teen Wolf.
My Summer Dragon is busy doing the Cabbage Patch.
My Minotaur is doing the "maniac" dance from Flash Dance.
The Green Thug Cat is doing The Twist.
My Inferno Cat has some B-Boy skillz and is doing handstands and some kind of break dancing.
My Storm Mander is doing the Russian folk dance (don't know what it's called).
My Jade Oni Helephant has got some massive hip shaking going on while my Pale Maiden and Yellow Ghost are busy working on their shoulder rolls and side to side action.
I think my Krok has the reincarnated James Brown moving through him.
The Storm and Heck Hounds are swaying and howling at the moon.
I still have not figured out what kinds of dances my Ghouls, Fang Bat, and Hydra are doing.
My Fire and Ice Elves plus the Sprite, Pixie Queen, and Dark Sprite move like they do in-game.
Please list anything else you have noticed about your pets. I have only been testing this out with my balance wizard (since the others who reached grand didn't roll over to test) so I have no idea what the other level 48 pets do.