Quaithe
One of the most interesting storylines in Game of Thrones season 2 and Martin’s novel A Clash of Kings involves Daenerys’ time in Qarth. While in the city, she and Jorah Mormont meet several interesting characters, including Pyat Pree, Xaro Xhoan Daxos and Quaithe. The season ends with the deaths of Pyat Pree and Daxos, but we don’t see what happens to Quaithe. In the show, she accurately predicts Jorah’s journey through Old Valyria later. She also knows he was Vary’s spy and warns him that Dany needs protection.
In the books, Quaithe gets more time and appears more often. She also has a stronger connection with Daenerys. In the books, she tells Dany ominous riddles about the future. Quaithe accurately predicts the plague that besets the people outside Meereen in A Dance with Dragons. She also warns her her of the “lion,” the “kraken,” and the “griffin” — she is presumably talking about Tyrion Lannister, Victarion or Euron Greyjoy, and Jon Connington. She also tells Dany a cryptic prophecy — “To go north, you must journey south. To reach the west, you must go east. To go forward, you must go back, and to touch the light, you must pass beneath the shadow.”
This prophecy is never brought up on the show, but Quaithe shows up several times in the books to remind Dany of it. Including this prophecy would’ve added another magical element to the show, and get fans wondering about what Quaithe wanted, what she knew, and who she was. So far, readers of the books don’t know any of those things, but some theories have been floating around. Unfortunately for show watchers, the series didn’t explore Quaithe’s character past season 2.