Treasure Goblin - I like to use this pet when I’m on my Warlock, for obvious reasons.
Forest Sproutling - I like to use this pet on my Warrior, because I have a toy that transforms me into a Forest Sproutling, and his name is Mini Krexen. We go on adventures together. 
I like the ones that float behind me, as if it’s some sort of spirit guide for my non-pet classes.
Floating Skull
The eyes, both Arcane and Dark Moon Fair
As a Shaman I used to really love the Geode, but Blizzard chose to ruin my experience by making it a ground pet, when pet battles come out, rather than letting it float.
Not one Geode floats Blizzard? Come on!
Mini Diablo (lord of terror) … because he is mini diablo (lord of terror)
Corehound Puppy. I named her Rosie and she goes everywhere with me.