Trying to compile something, this is what I have so far with help from various people on the WoW Subreddit:
(Italics denotes unconfirmed or speculated)
Druid
Feral - Increase 3% movement speed out of combat.
Balance - Ancient and powerful magic has affected this creature. Only a powerful Druid wielding the Scythe of Elune can dispel the effect. & "Feral Worgen" out in the Broken Isles (neutral) that you can de-curse with the Balance Artifact.
Restoration - Treant in Dalaran tosses an apple when he recognises G'Hanir. Flowers growing at feet when still.
Guardian -
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Paladin
Protection - Allows you to see hidden demons.
Retribution - When you kill a demon or undead, they turn into ash. Chance to instantly kill on an auto attack (white[sic]) swing.
Holy - Increased damage by 100% against Undead.
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Hunter
Marksmanship - (Stacking) Speed buff.
Survival - Eagle called to aid under 40% health. Turn into eagle when dead/ghost.
Beast Master -
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Warrior
Fury - Ressurected by Odyn, must kill within 8 seconds to stay alive.
Arms - Fear trolls.
Protection -
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Death Knight
Frost - Growing frost patch on the ground while standing still.
Unholy - Chance on kill to leave the enemies rotten corpse discolored and swarming with flies. Chance on hit to finish off enemies below 20%.
Blood - Stacking 30 second buff every time they kill something. Each stack gives a 1% damage increase and I assume it stacks infinitly long as you kill something else before the 30 seconds is up, max 10%.
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Mage
Fire - Corpses burn.
Arcane - Flat 2% damage increase in Broken Isles. whispers to you every now and then, when you use certain abilities
Frost - able to speak to an NPC in Dalaran (pretty certain it's only Frost Mages since the NPC remarks you have Alodi's staff) which gives you a 2hr buff that increases XP and Rep gains by 5% in the Broken Isles.
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Monk
Windwalker - Knock back effect on some attacks, when jumping from a certain height. approx 1.5x jump height
Brewmaster -
Mistweaver -
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Priest
Discipline - Chance to do "massive" damage. Smite builds up over time and then unleashes on a random cast. Approx 20 minutes.
Shadow - Blade whispers to you.
Holy -
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Rogue
Outlaw - 2% Movement speed increase upon killing lasts 30/60 seconds.
Subtlety -
Assassination -
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Shaman
Elemental - Certain air elementals in Stormheim become friendly.
Restoration - Watery ground effect, and start kneeling when AFK
Enhancement -
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Demon Hunter
Havoc -
Vengeance -
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Warlock
Affliction - Killed enemies can leave behind a purplish soul.
Destruction -
Demonology -
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If anyone has anything extra or any corrections, please let me know.