Hippogriffs (or Hippygryphs) shouldn't exist. The Hippogriff is the offspring of Griffin and horse. Why shouldn't they exist? Griffins feed off of horses. And yet, here they are! The most commonly known hippogriff of course, would be Buckbeak from Harry Potter. (I always loved Buckbeak!)
Hippogriffs (from what I have read, I do not know for sure as of I have never played the games) also are in World of Warcraft (WoW) as Flying mounts for hire and also Final Fantasy.