Macall B. Polay/HBO
Some notable differences included a love triangle between Arya and Jon Snow, a marriage between Sansa and Joffrey (and a baby), and Jaime Lannister sitting on the Iron Throne.
According to Martin's original outline, Jaime ends up killing everyone that comes before him in the line of succession in order to become the king of Westeros.
Here's the excerpt from Martin's original "Game of Thrones" outline describing Jaime's rise to power:
"Tyrion Lannister will continue to travel, to plot, and to play the game of thrones, finally removing his nephew Joffrey in disgust at the boy king's brutality. Jaime Lannister will follow Joffrey on the throne of the Seven Kingdoms, by the simple expedient of killing everyone ahead of him in the line of succession and blaming his brother Tyrion for the murders. Exiled, Tyrion will change sides, making common cause with the surviving Starks to bring his brother down, and falling helplessly in love with Arya Stark while he's at it. His passion is, alas, unreciprocated, but no less intense for that, and it will lead to a deadly rivalry between Tyrion and Jon Snow."
Jaime is, of course, not sitting on the Iron Throne in the HBO show, but is now standing alongside it while his sister and lover Cersei, who rules the Seven Kingdoms. But the series isn't over yet, and as Cersei continues to execute more and more violent and ill advised plans that threaten the destruction of King's Landing, perhaps the Kingslayer in Jaime will be invigorated once more?