You can have the dog search for various random herbalism ingredients, while the wolf will bring back things like meat and traveler's supplies. You can have the do sit and call him a good boy. The other animals don't have anything you can do at home and are more used for cutting down on your traveling time and helping you fight.
Tangentially related: I think it'd be cool if you could tame a dire rat. There's already a rat lure, and it could bring you stuff like bones, nuts, mushrooms, and roots. I think it'd be cool.