The kikwis were so plush and adorable! I loved the noises that they made (kyooo kyooo). Also, the cats and dogs from Twilight Princess. For hours, I would literally do nothing but pick up cats and have Link run around the town like a crazy person.
I like Skyward Sword's Remlits. I think they're cute even at night when they're psycho. (I know real life cats that are like that sometimes).
I love the dogs and cats in Twilight Princess. I think it's adorable how the cats (especially the kittens) will follow you around.
I love the baby chick in Oracle of Seasons. It's in Malon's house. You go there and there are cuccoos and there's this one baby chick that will follow you around and try to get close to you.
Link himself in Wind Waker is endearing with his little "Hyup!" when he jumps down from things, and I adore Aryll and Medli and Makar.... and Grandma - Let's just say that most of Wind Waker can compete for "cutest thing I ever saw in a Zelda game." The whole game is made of cute.
Romani's constant bickering with her older sister in MM. In a way, if you view it from Cremia's side it can be a little sad, but from Romani's POV it is basically just one of those "I'm her little sister so she has the responsibility to take me wherever I go" sort of things. It's cute to me, anyway. :3