I would really love to see companions that are non-humanoids and that there would be more than 1 of them in the game, perhaps a merchant that trains dogs to protect humans, some that are trained for hunting and spotting enemies and such. It would be really cool to sneak in the forest, my hunting dog with me to spot enemies for me. When there would be human enemies, the dog would growl and when there is an animal nearby it could lay low with it's ears pointing straight up. Depending on how well it has been trained, it could show more signs that you can learn to anolyze to know what is on the other side of a rock.
Other possible pets could be a hunting falcon, flying above you, flying in circles above enemies so you knwo where they are.
Would you like to see pets in Skyrim, some that would help you in combat like a really touch guard dog, and others that simply give support as spotters? Maybe find your lost arrows for you if you miss the enemy?