All right, two more classes!
Warlocks will get an up-to-date Dreadsteed of Xoroth-like mount (like the Paladin mount, this one flies without any visible wings, just glowing hoofprints.) You speak with the guy who collected materials for the original mount quest (that got 86'd in Cataclysm) and he sends you to do a number of things.
There's some auction house stuff - a potion, some metal, and some gems - and a pretty quick collection of Moonkin blood from a place in Val'sharah, and then the thing that will probably be frustrating to you if the stars have not aligned: an item off of the final boss of an invasion scenario.
With that stuff gathered, you get a quick quest to on the Broken Shore requiring the use of your Succubus and then you get to go into one little solo-scenario that has you slaying demonic minions (that go down easier with a Felhound) before taking out an eredar and enslaving its demonic horse, which you then get to claim.
The Mage mount has less set-up, requiring you to gather three pieces of a device Antonidas was working on before he died. These require a little bit of combat but mostly just ample use of teleportation and using Dalaran's central tower portals.
Once you get all three pieces, you go to the Eye of Eternity and have three somewhat challening fights against the elemental energy trapped in each fragment. Once all three are defeated, the three pieces are linked together and you get your cool flying disk.