Griffons are now thought to be extinct, though they once served as mounts for the Grey Wardens, who still use a griffon as their symbol. The number of Griffons slowly dwindled after the fourth Blight, finally becoming extinct 200 years prior to the outbreak of the Fifth Blight in 9:30 Dragon.
Some of the armor that was used by the Grey Warden griffon riders can still be found in the Grey Warden's item stash in Denerim.
In real life, griffons are dogs. The mentioned creatures are griffins, the mythological creature which has a lion's body and an eagle's head and wings. They are sometimes painted as double-headed, but mostly single.