The Seven Kingdoms were united by the Targaryens. They united the first six because they had three huge dragons. Dorne was brought into the fold because the Targs could call the combined might of the other six kingdoms to subdue Dorne.
I'm going to assume here that either Bran, Jon, Dany, Sam, Davos, Thoros, Marwyn, Victarion's Red Priest (his name escapes me) or Arya will find a way to defeat The Other. This will be a very messy process. I believe most, if not all, of the North will be only smoking ruins by the time this is accomplished. The Others may march all the way to The Twins. (Most of us would like to see the Freys get theirs.)
But when The Other is defeated, certain political realities must be faced. The savior... TPTWP, the three-headed dragon, the Stallion who mounts the World, Azor Ahai reborn... whoever... will be in a position to at least claim a portion of the Seven Kingdoms for his/her own.
Another reality is that neither the Tyrells, the Lannisters, the Arryns, nor the Martells will have their lands, their armies, or their economies destroyed by the Others. They'll still be strong and given their proximity to King's Landing, they'll have a major say in who rules there. The Lannisters, the Martells, and the Arryns all ruled independent kingdoms before the Targaryens... while the Tyrells were promoted to fill the vacancy of the Gardener family... made extinct by dragonfire. All of these realms were invaded, conquered, liberated, restored, etc... except for the Vale. The Arryns are legendary for remaining independent for over three thousand years. The only power to subjugate them did so with dragons. And so I contend that Dany is the only one who can rule a united Seven Kingdoms...
...that or Euron actually is able to control dragons with his horn. Even though he could theoretically unite the Seven Kingdoms with his dragons, I shudder at the thought...
The Ironborn ruled and raided the Riverlands for millennia. The Riverlands may belong to the Crown, the Iron Islands, Harrenhal, or Casterly Rock, but I think it will suffer from wars, raids, and banditry for decades to come. The only hope for the Riverlands is Dany... and her dragons.
The other reality is that the Targaryens will have returned. Will they unite or will they fight each other? If they fight, then I don't know what will happen. And if Dany dies then the Seven Kingdoms will remain fragmented.