The mythological griffin could be seen as an example of this. Part lion (king of the animals) and part eagle (king of the sky) would make it rather awesome for the medieval noble class.
The chimaera. It's a lion. And a goat. And a dragon. Why? Just 'cause.
One could argue that it was thusly named so as to provide the title of an NCIS episode, solely for the purpose of the fantastic line, "They did not name it 'The Puppy.'"
Ancient Egyptian Mythology had creatures like this. They were made up from the parts of ferocious and dangerous animals to, well, depict them as ferocious and dangerous.
Tawaret had a lion's head and limbs, a pregnant hippopotamus's body, a crocodile's backside and tail, and sometimes carried a knife. She was a goddess that protected pregnant women and new mothers from any complications.
Ammit had a crocodile's head; the mane, front body and legs of a lion; and the hind body and legs of a hippopotamus. She was a demon of the underworld who ate the unpure hearts of deceased ancient Egyptians, thus damning them to nonexistence
The Nue of the Japanese mythology has a monkey's head, a tanuki's body, the legs of a tiger, and the tail of a snake (or alternately, a snake as tail). To complicate matters, it is said to have the call of a thrush, which at a certain period of time is also called Nue.