Cenarion War Hippogryph

The Cenarion War Hippogryph is a special flying mount available to players who obtain Exalted reputation with the Cenarion Expedition. It was the first hippogryph mount to be added to the game.

Source
This mount is sold by Fedryen Swiftspear, the Cenarion Expedition quartermaster, at the Cenarion Refuge in Zangarmarsh. It is ridable by players who have a riding skill of 300. Its cost is ( with the Exalted discount of 20%).

Wrath of the Lich King
In WotLK, as of patch 3.2, two other hippogryph mounts exist, the Silver Covenant Hippogryph (mount) and Argent Hippogryph. Each is available from vendors for after completing certain quest and reputation requirements However, the Silver Covenant Hippogryph (mount) is only available to the Alliance.

In patch 3.3, animations for standing on the ground, walking, and running were added to all hippogryph mounts. Prior to this patch, hippogryphs would simply hover at ground level (with a speed reduction as with all flying mounts), much like nether rays.