Spoilers all over the place until volume 5.
The most common theories for the end of A Song of Ice and Fire all go something like this: three Targaryens riding the three dragons — just like when they first conquered — will sweep over Westeros and kick the Others' ass. While this theory seems confirmed by the subtle hints of who the two other Targaryens could be — in aDwD, it is no longer a hint — I no longer adhere to it.
Still, the number three clearly plays a central role. Three surviving Targaryens, three dragons, three Great Houses… Wait, what? There will definitely be three of something.
But “everyone behind the Targaryens”… TWhat about Tyrion? He becomes a mere advisor while this newcomer Aegon — if even he is genuine — gets to ride a dragon? How is that fair? Well, GRRM does not care about fair. How is that satisfying?
And even Jon Snow: he's secretly a Targaryen so that makes it ok? No. Whatever the genes, by education, by spirit, Jon Snow is definitely a Stark. Jon Snow and Daenerys are not the same person, they have their own personality, they are very different from each other; they are both awesome, but not in the same way. While I am sure a lot of fans would love him, the story does not need a male Daenerys.
The story insists many times on how House Targaryen is special, but is it really?
We are frequently told how centuries of inbreeding led the Targaryens on the fine line between greatness and madness. Well, Geoffrey, how is that for madness and inbreeding? And Arya, does she strike you as perfectly sane?
The Targaryens have dragons and can walk into the fire, but the Starks have direwolves and are wargs. That seems pretty special too.
There is another weakness with the Targacentric theory: it does not leave room to weave in the huge question: what was the Doom of Valyria? The reign of the Targaryens on Westeros lasted for about three centuries; the cycle of struggle with the others covers millennia. It is a mistake to look just at Aegon the Conqueror to guess what will happen beyond the wall.
The crux is, this story has three heroes from three Great Houses, and everyone else more or less revolves around them. Even Stannis' army, in the end, is only a loose canon.
To defeat the Others, all Houses must act united around the three major Great Houses, all three equal in importance and authority.
Three Houses, three heroes, choose how you like it better: passionate, brooding or cynical?
Each House brings its own kind of fire to the Song: the Fire of Honor (or possibly Justice?), the Fire of Conquest and the Fire of Protection. The heroes have their dominant fire, but all partake of all three to some amount: Jon Snow dedicates his honor to protecting the realms of men and has the charisma to lead; Daenerys wants to keep what she conquered and rule it fairly.
The other, characters show other kind of fires, variations on the themes. With the less heroic ones we can see what happens when the Fires are out of balance. In Arya, Justice has become punishment and then vengeance. Cersei shows us what the Fire of Protection is when it does not have the Fire of Honnor as a moral compass and Lysa would have needed some Fire of Conquest to stop being so overprotective.
All three Fires have their dark side. The Judge must not hesitate to pass stern sentences, that was the very first chapter. The Conqueror must sometimes be cruel to inspire fear to her enemies. The Protector must be ready for distasteful but necessary actions, like killing the king you are sworn to protect.
The story shows us how the forging of the champions for each House, and the bonds between them that will create a strong lattice of loyalty: Tarth to Tully and Stark, Mormont to Targaryen, Tarly to Stark, Seaworth to Baratheon, etc. The characters are subjected to painful trials that expose their inner weaknesses so they can overcome them. Sometimes they break, like Oberyn leaving a fatal opening to the Mountain out of pride, and the forging must start anew.
This theory does not predict much in practice. It serves more as a perspective to read the story. I could predict a finale with a big eigenplot for all houses, but it would be too nice and shiny for that kind of story. Let's RaFO.