What Significance Does the Number 7 Have on Game of Thrones?

Game of Thrones is based on George R. R. Martin's book series A Song of Ice and Fire, and even though we're still waiting on the sixth book, when he's finally done, there will be six volumes, as follows:

1. A Game of Thrones
2. A Clash of Kings
3. A Storm of Swords
4. A Feast For Crows
5. A Dance With Dragons
6. The Winds of Winter (not yet published)
7. A Dream of Spring (not yet published)