Dragons Hmm, I like nearly all living things for one reason or another. I like fungi in particular though, for whatever reason. They're quite fascinating and many species of them are very beautiful; I also couldn't imagine a good fantasy setting without them. Snails & slugs are nice, too, and leeches are interesting.
Besides that, water deer and musk deer are amazing, mainly because of the "fangs"; I'm not even sure why, but I love teeth like that. Cows, megabats, caracals, manatees and aye-ayes are all awesome for one reason or another, too. Also elephant birds and moa, also they're not really "living things" anymore. All sorts of turtles, too... I should better stop now or I'm going to end up listing every non-human living thing in existence in the end :p It's just so hard to decide on favourites when so many creatures are so wonderful in their own way.