Mage quests

Quest for Teleport: Dalaran
Can be obtained at level 71.

Quest chain for Robe

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Quest chain for Mage's Wand
Can be obtained at level 30. Starts at mage trainers in capital cities and directs you to Tabetha, a witch in the middle of Dustwallow Marsh.

Quest progression for Celestial Orb or Celestial Stave
Can be obtained at level 35. Starts at mage trainers in capital cities and continues with Tabetha, who again gives a series of challenging quests.

Quest chain for Glacial Spike, Arcane Crystal Pendant or Fire Ruby
Can be obtained at level 50. Once again, mage trainers in the capital cities will direct you to Archmage Xylem for this quest chain.
 * (optional lead-in)

Quest for Spell: Conjure Water (Rank 7)
Starts at Lorekeeper Lydros in the Library in Dire Maul North.