Creatures-Hippogriff

Half Horse, Half Eagle, the Hippogriff is a magical creature native to Europe that somewhat resembles a Griffin, except the lion rear is, instead, a horse's. 

'Easily offended, Hippogriffs are. Don't never insult one, 'cause it might be the last thing yeh do.'-Hagrid-Harry Potter and the Prisoner of Azkaban.

Buckbeak is, of course, the most renowned of these, first appearing in the series as one of Hagrid's creatures for the Year 3 Care of Magical Creatures class, and later being used to help Sirius Black escape, and living with him for a while after that.