kakapo and takahe -- two flightless birds from New Zealand
hoopoe -- another bird with a fun name
star-nosed mole
elephant shrew
elephant seal
thylacine
thylacoleo
tuatara
archer fish
peccary, a.k.a javelina

How about invertebrates?
peripatus, a.k.a. velvet worms, phylum Onychophora -- freakishly strange
hydra polyps that asexually bud jellyfish that sexually spawn more hydra
sphinx moths
ant lions
horseshoe crabs