Also, recently I went through a round in the Game of Thrones mod for Crusader Kings II. I started in the Clash of Kings scenario (as everyone's favorite character DARKSTAR) that takes place near the beginning of ACoK and quit at 350AL (50 years after ACoK). The mod doesn't work now with the recent CKII update so I can't pull up specific details, but there were a few amusing things and alternate scenarios that played out:
Robb Stark loses his independence war when Balon invades. North becomes vassals to the Iron Islands. Balon reigns as King of the Iron Islands and the North for quite a while until he dies a natural death and Theon takes over. Robb dies a natural death about 30 years later. The Iron Islands manage to conquer the Vale for a while and Victarion is Lord of the Vale for a brief time. They fail an invasion of Dorne though. Near the end, the Greyjoys are usurped by some other family and lose the title of King of the Iron Islands, but they are still hold the Kingdom in the North.
Stannis is defeated by Joffrey, but lives out the rest of his life on Dragonstone. Joffrey reigns for about 10 years until Aegon VI attacks and takes the throne from Joffrey. Joffrey rules over the Stormlands until he is mysteriously assassinated, and then Tommen is in charge.
Aegon VI marries Dany, who dies at the age of 26 from the bloody flux. The Iron Throne also controls Meereen. Aegon strips the Tyrells of Highgarden and gives it to someone else. Aegon later remarries and his heir, Aegon VII, takes over when he dies after reigning for about 30 years.
Tywin dies a natural death in 300AL. Tyrion takes over the Westerlands. Jamie has a rather crazy adventure, from being in the Kingsguard, to being a prisoner in Dorne, to eventually ruling the Westerlands. He has a daughter with some random girl named Sabrina Lannister. After the child Aegon VII becomes king, Sabrina Lannister and her allies wage a war for the throne and win. Aegon VII rules over Dorne, clamoring for his throne.
Wildlings defeat the Nights Watch and take over the wall, but don't push past the Gift. Jon Snow dies naturally after doing nothing. NW eventually retake the wall.
Loras becomes the leader of the Kingsguard and slays a dragon.
Darkstar (me) kills Sweetrobin in battle after the Iron Islands invade Dorne.
There, just saved everyone 3,000 pages worth of reading.