Also the ONLY way Brienne and Davos may work is if Stannis is alive. Yes, Davos would be pissed Shireen was killed, but he is loyal to Stannis the way that Brienne could only dream about being loyal to Renly.
I can imagine Brienne meeting Rickon: “HELLOIAMACRAZYPERSONWHOKNEWYOURMOTHER.WON’TYOUCOMETRAVELWITHMEIPROMISEIWON’TMURDERYOULIKESOMANYPEOPLEHAVE.” She needs some people skills.
And then she’d probably unsheath Oathkeeper and say “Jamie Lannister gave me this sword to remind me to find your sisters” 
Sparked by the post about Jaime Lannister’s story being essentially over…
What if he ends up on the throne? It would certainly be a surprise (on events so far) but he’s a major character that has existed in the books from the start. and I really think it has to be someone like that. In fact, that why I basically snorted when I first read about the fake-dragon kid. No way would a decent story ring in the ultimate protagonist in a series in Book 5. Or 4, I forget which it was.
Anyway, wouldn’t that be an amazing story arc? You start with someone the readers genuinely despise – a sister fucker, a man who casually tried to kill a little boy, one we learn was reviled by most as a king slayer – and then you bit by bit let some good aspects show/develop, then you maim him, taking away the essence of his self-image as Mighty Fighter – and then <lots of stuff must happen> and in the end he somehow saves the day and ends up as King.
Wouldn’t that be a shocker?
How exactly would Jaime end up on the throne? It’s not as if the people are going to rally for the “Kingslayer” and he has literally no claim. And I don’t think he’d actually want it as well.
That’s the <lots of stuff must happen> part. 
As for the inheritance claim, um. Well, tons of sons inherit thrones from their father, the king. Maybe he can inherit the throne because he was the father of the king. Twice over!
Pshaw. Like GRRM has EVER cared about giving his characters what they want.
Interesting idea, if a little far-fetched. But (in the books) I think it’s very likely that Tommen and Myrcella are not long for the world. Stannis and Shireen would be next in line (as far as the general Westeros public knows), but season 5 leads me to believe that they won’t be around in the books much longer, either.
So who would inherit by popular/noble will? One of Robert’s bastards, perhaps? I think it’s more likely that, if the incest kids + Stannis and Shireen die, fAegon actually ‘wins’ his war (by default) and takes the Iron Throne (some prophecy’s “mummer’s dragon”), before Daenerys sweeps him away.
Or Westeros devolves into the old Seven Kingdoms, with Jaime (assuming he survives) as King of the Rock (and a Tyrell as King of the Reach, Robin/Harold Hardying in the Vale, who-the-hell-knows in the Stormlands and Riverlands, some surviving Stark in the North, Martells in Dorne, and a Greyjoy in the Iron Islands).
But would Dany sweep away Aegon? If the rumors of Aegon being a Blackfyre are correct, a marriage would reunite the two Targaryen sides (and even if Aegon was a true Targaryen, marrying family is a tradition).
Same way as in the books:
He killed the king. Then he sat down on the throne. I don’t remember why he did it (or at least his justification in his telling). I also don’t know what his claim would have been as compared to Tywin, or Ed Stark, or Robert who ultimately got it. But suppose he’d have said “fuck it. I killed the king. I’m on the throne. It’s mine.”
And suppose that happens again?
Robert got the crown because the Baratheon’s are the closest family in Westeros to the Targaryen dynasty - Robert’s grandmother was the daughter of Aegon V.
Saying fuck it, I killed the king, the throne is mine would have likely have resulted in him getting killed - you kind of need a base of support… or a massive army.
Jamie’s story is not over until Cersei kills Tommen and Jamie kills her.
I kinda like the idea of Jaime becoming king. He would be a sadder, wiser man than before, and it would be a clever callback to when he first sat on the Iron Throne after having slain the Mad King. I agree that a LOT of stuff would have to happen before he could do it, though, and it would have to be by right of conquest rather than by any persuasive dynastic claim to it.
Jaime would never want to be king. Besides, he’d be lacking a Hand.
*rimshot
If Westeros were Western Europe… not perfectly analogous, of course, but some interesting parallels: This Map Of Westeros Shows The European Equivalents Of The Seven Kingdoms | HuffPost Entertainment
Pretty decent map, but Wales for the Stormlands is a bit of a quibble. The Stormlands while rocky, green, and wet were also quite militaristic prior to conquest. So perhaps more like Denmark (which actually did conquer quite a bit of territory in the Medieval era)?
I am finding myself VERY curious about where Sansa’s story is going to go in book 6 now. Brienne’s too for that matter.
Sansa could die on p. 1 of The Winds of Winter and I wouldn’t particularly care. Brienne, though… ah, Brienne. She’s a favorite of mine. Hope she’s got lots of adventures and knight-errantry ahead of her.
By the way a Sansa chapter from Winds has already been posted to the web. So we have some idea where that story is headed.
Hardyng FTW!
Man, Harold is really going to kick himself for being snooty towards “Alayne” when he realizes that she’s actually Sansa Stark ;).