Profession mounts

Profession mounts that are available from most of the professions in the game, whether primary or secondary.

Alchemy

Alchemists can use archaeology to find a recipe that will teach them to create [Vial of the Sands]. The vial teaches players how to turn into a Sandstone Drake, a flying mount that allows for one passenger.

Sandstone Drake

Archaeology

The [Fossilized Raptor] requires 150 skill to find and 100x Fossil Archaeology Fragments to solve.
The [Scepter of Azj'Aqir] requires 450 skill to find and 150x Tol'vir Archaeology Fragments to solve.
The [Spirit of Eche'ro] is a quest reward from the Archaeology quest, [45] Laying to Rest.

Fossilized Raptor
Ultramarine Qiraji Battle Tank
Spirit of Eche'ro

Blacksmithing

Blacksmiths can craft the [Steelbound Harness], which teaches the Steelbound Devourer mount.

Steelbound Devourer

Engineering

There are two flying machines that can be crafted and used only by engineers.

Flying Machine (airborne)
Flying Machine (landed)
Turbo-Charged Flying Machine

Engineering also allows a character to create a faction-specific ground mount that can carry one passenger. Unlike flying machines these bikes can be used by non-engineers. Obtaining this mount awards the achievement [Get to the Choppa!].

Mekgineer's Chopper
Mechano-Hog

Engineers can learn to create a rocket mount based on their specialization, which can be sold to non-engineers. Gnomish engineering can only make the [Geosynchronous World Spinner], while Goblin engineering can only make the [Depleted-Kyparium Rocket].

Geosynchronous World Spinner
Depleted-Kyparium Rocket

There are also other unique flying mounts that engineers can learn and sell to other players.

Sky Golem
Mecha-Mogul Mk2

Fishing

The [Sea Turtle] can be fished from some zones, Shipwreck Debris around Darkmoon Island or can drop from a Lunarfall Cavedweller / Frostdeep Cavedweller with a Level 3 Fishing Shack at the garrison.
The [Brinedeep Bottom-Feeder] can be purchased for 100x [Drowned Mana], which the mana can be fished from Margoss's Retreat.
The [Darkwater Skate] can be purchased for 500x [Darkmoon Daggermaw], which these fishes can be caught in the Darkmoon Island ocean waters.
The [Pond Nettle] can be fished from the fel pools in Krokuun and Antoran Wastes.
The [Great Sea Ray] can be fished from the ocean waters surrounding Kul Tiras and Zandalar.

Sea Turtle
Brinedeep Bottom-Feeder
Darkwater Skate
Pond Nettle
Great Sea Ray

Jewelcrafting

Jewelcrafters can learn to make five jewel panther mounts that can be sold. The first four are the [Jade Panther], [Sunstone Panther], [Ruby Panther] and [Sapphire Panther]. The first four are then themselves used as mats to create the [Jeweled Onyx Panther]. This means to have all five, the first four are created twice, one set to be mounts, and another set as mats.