Hi there - I'm new to this thread, but not the show, or the books (both of which I love, although the latter a bit more, particularly since the former has had to speed off on its own).
I just wanted to share my prediction of who will end up on the Iron Throne. This is the first time I think I've been able to read between the plot lines to get a good rationale - rather than just guessing outright.
I note flicking back through this topic, some of you guys had some good success at guessing what was going to happen previously here - so keen to know what you think of it! I'll put spoilers is as I'll reference a point from the books (which people up to date with the TV series may be unaware of).
I came to this conclusion* only recently, and rather indirectly - bear with me on this! After the last TV episode some friends of mine were speculating the Jaime might be the one to kill Cersei. This isn't totally implausible given how they parted. It also fits with Maggy the Frog's prophecy: that the Valonqar or "little brother" (as Cersei was later given the translation by her Septon/Septa I think) would be the one to kill her. Although Cersei has long assumed the threat is Tyrion, Jaime is the younger of the twins, so could fit the description.
However, I don't think Jaime will want to go back to King's Landing (in the show, or the books). Everything for me points that he wants to finish up doing something honourable. He's been itching for the opportunity as he feels resentful at being reviled as the king-slayer for dispatching Aerys, despite saving the whole city in the process. I don't think adding kin-slayer to the list is what he'll want. The army of the dead is the clear-cut good-versus-evil battle he's been looking for all his life.
So if it's not Jaime who will kill Cersei, then who? Maggy got everything else spot on, so her demise seems inevitable. When following that thought process it occurred to me that the Valonqar may be another one of those Valyrian words that is genderless - perhaps "little brother" is a faulty translation, and should be "little sibling" - much like the confusion with the prince/princess that was promised prophecy.
If Cersei's killer is female, then that brings Arya potentially into play. That kill list of hers has been repeated too many times not to be a more significant plot element in my estimation. So far only relatively minor characters have been dispatched (Walder Frey's infamy for the Red Wedding aside). Now, it should be noted of course, Cersei has no sister. However, she's been assuming that the "Valonqar" is her little brother. However, in the prophecy, I believe Maggy refers to "The" Valonqar, not "Your" Valonqar.
So what if it isn't the Valonqar of Cersei herself, but rather the younger sibling of the one "younger and more beautiful, who will come to cast her down and take all she holds dear", also mentioned in the prophecy. Given Cersei is the current occupant of the Iron Throne (at least in the TV show), presumably this refers to an usurper / successor. Who is Arya the younger sister of, and might fit that description?
Cersei had been falsely guessing Magaery, whilst for many fans it was "obviously" meant to be Dany. GRRM doesn't do obvious though.
To add to this, in both the shows and the books it is noticeable her political credibility has been slowly building. Particularly in the show, she has now had both Littlefinger and Ramsay dispatched - arguably people she both learnt and suffered from. Notably however, getting other people (or animals) to swing the sword (dagger/teeth) - not the way of her father. In the show she's also made a point of how much she learnt from Cersei - making her a logical next target in the pattern of Sansa's progression. A likely trigger for action could be when her betrayal after feigning a temporary alliance is discovered. Sansa's story and character development also feels like it's gearing up for her wanting power more and more.
You also have to ask why Maggy uses one, and only one, Valyrian word in all her answers to Cersei's questions. Surely that's significant, and the only explanation I have is that's it's designed to conceal something. I think it would also be quite amusing if in fact Jon is the prince who was promised, and the discussion around gender confusion (identified by Maester Aemon / Missendei in the books /show) is in reality not relevant for that application. Rather it is just giving the fans the knowledge they need to potentially decipher a different clue.
The only thing that makes me doubt this theory is that I don't think the Valonqar is actually mentioned in the TV show flash back, only in the books. This leads me to ask why they would cut it, if it is that significant? I guess though explaining how Cersei found out the translation, and her fears around it, might have been too tricky for the TV medium (without being able to hear her thoughts etc).
*probably someone (really annoying) has already come up with this on internet somewhere, although I haven't seen it yet.