None. Animals are ugly, smelly, dirty, dangerous creatures even when they are young, and they tend to make a mess in any environment populated by humans. Then again, with the exception of the dangerous part, so are human babies, which is why I don't think of them as cute either.
The only way something can be cute is if it doesn't stink, doesn't eat, doesn't excrete anything, but is pleasing to the touch. In that case I'll take a stuffed toy mammal any day. There's no preference of animal choice there.