The following mounts are available through various branches of the archaeology profession. So far, there are four.
Fossilized Raptor – requires 100x fragments
Flavour text: Legends tell of a spell placed upon a hunting raptor who dared to snarl at young Tyrande Whisperwind as she bathed in a jungle pool. The beast is cursed to wander Azeroth – until it apologizes.
Where to dig? Kalimdor zones
Scepter of Azj’Aqir – requires 150x fragments (including up to 3x Tol’vir Hieroglyphics)
Flavour text: The aqir were a race of incredibly evil, expansionistic insects who battled the troll empires for thousands of years. Eventually, the great Azj’Aqir civilization split in half, with Azjol-Nerub in the north, and Ahn’Qiraj in the south. The night elves were able to contain the qiraji for many years until they were awakened again by the Old God C’thun.
The Tol’vir sorcerer Azj’Aqir was said to possess a scepter that would allow him to control a Qiraj battle tank outside of its Silithus home.
Canopic Jar – requires 45x fragments (including up to 2x Tol’vir Hieroglyphics)
The jar has a small chance to contain the Vial of the Sands recipe that only alchemists can see. This mount teaches you how to transform into a dragon, allowing you to carry an ally on your back.
Where to dig? Tol’vir dig sites are exclusive to Uldum (Cataclysm expansion)
Spirit of Eche’ro – one of the archaeology questlines from Dalaran leads you into Highmountain to recover the bone fragments of Eche’ro.
Flavour text: The spirit of Huln Highmountain’s pet moose.
Pick up the quest – The Right Path from Dariness the Learned in Dalaran. It will take ~3 hours to dig 600 bones. This quest will appear on the 15th of February, then every six months. (see video)
Where to dig? Highmountain (Legion expansion)