Ancient Mana - Currency used in Suramar for quests, NPCs, purchasing from special vendors. Progressing through Surmar story-line will increase carrying capacity to 1500 and an additional 500 for finding hidden items around Suramar. For specific locations on the items and more information check varenne's comment.

Brawler's Gold - Currency used by the Brawler's Guild to purchase from NPCs. For more information check Kandango's comment or the Brawler's Guild Overview.

Blood of Sargeras - Although not exactly currency it is used to purchase crafting materials and order hall resources from Illnea Bloodthorn (don't worry about taking them out of the bank the game automatically keeps track of how many you have when used will take out of both inventory and bank if you don't have enough in your inventory). For more information check Steiner14512's comment or Acquiring and Spending Blood of Sargeras and Obliterum.

Coins of Air - (Rogue only) Currency used by Rogue vendors obtained through pick-pocketing and missions from the class hall through specific followers. For more information check kodora1316's comment.

Curious Coin - Currency used to exchange goods from Xur'ios. Check the jjanchan's comment for more information on what is sold and how to obtain Curious Coin.

Echoes of Battle - Used to purchase non elite pvp gear from Marshal Frazer (Alliance) or Violet Shadowmend (Horde). Obtained through obliterating non elite PVP gear in the Obliterum Forge.

Echoes of Domination- Used to purchase elite pvp gear from Marshal Frazer (Alliance) or Violet Shadowmend (Horde). Obtained through obliterating PVP elite gear in the Obliterum Forge.

Legionfall War Supplies - Currency used to construct the three buildings on the Broken Shore. These are obtained primarily through WQ on the Broken Shore and other content on the Broken Shore.

Lingering Soul Fragment - Collected for the quest Soul Prism of the Illidari. Obtained from killing the last boss of a Legion Dungeon.

Mark of Honor - Although these are a currency they take up a slot in your inventory / bank (don't worry about taking them out of the bank the game automatically keeps track of how many you have when used will take out of both inventory and bank if you don't have enough in your inventory). These are used to purchase old PVP gear / transmogs along with heirlooms from various vendors. They are obtained through PVP and PVP WQs. For more information check out leobolin's comment.

Order Resources - Currency used to on Class Hall Missions, Artifact Research, and various other Class Hall related content. For more information check Steiner14512's comment or Acquiring and Spending Order Resources.

Seal of Broken Fate - Currency used to re-roll World Bosses, Mythic Dungeon Bosses, and Raid Bosses loot table. Only 3 can be obtained a week (excluding getting it from Class Hall Missions) with a maximum of 6 being held at any given time. The three weekly Seal of Broken Fate are obtained from Archmage Lan'dalock for Gold, Order Resources, and Mark of Honor. For more information check jjanchan's comment.

Sightless Eye - Currency used in The Dalaran Sewers. Obtained through doing content in The Dalaran Sewers *note The Dalaran Sewers is a marked pvp zone*. For more information check jjanchan's comment.

Timeworn Artifact - Currency used for a quest to gain Reputation in Azsuna from King Mrgl-Mrgl. It is acquired through looting creatures at the Timeworn Strand. For more information check HobDawgh's comment.