Originally Posted by
Wyrt
Night elf mages are highborne or those taught by the highborne. The highborne were recently re-accepted back into night elf society by Tyrande. They're generally looked down upon by other night elves. Some night elves, like Maiev, even outright kill them on sight.
Blood elf mages are the magisters. They operate out of Silvermoon. The Sunreavers were a group of blood elves that worked out of Dalaran, but Jaina kicked them out. The Sunreavers have since been integrated into the magisters under the command of Grand Magister Rommath.
Orc mages were trained by forsaken I believe. Not sure how they're viewed in orc society.
Draenei should have a mage school or organization somewhere, they just haven't been showcased yet in WoD. We do see the artificers who work heavily with arcane based technology, but artificers can be any class, not exclusive to mages.
Pandaren disapproved the night elves' use of arcane, so I'm not sure what the story is with panda mages.
I believe dwarves are just Kirin Tor mages.