Lots of theories concerning ASOIAF are major tinfoil, but there are some that actually make sense (and have since been confirmed).
R+L=J, or Rhaegar Targaryen + Lyanna Stark = Jon Snow is probably the best-known ASOIAF theory of all time. R+L=J was generally acknowledged to be true, mostly because of the overwhelming evidence in favour of the theory. The Tower of Joy sequence during one of Bran’s visions in S06E10 finally confirmed the theory, but everybody knew it was coming.
2. The Knight of the Laughing Tree
On the subject of Lyanna, one of the biggest events in support of R+L+J was the Tourney at Harrenhal. In a story Howland Reed told his children, a mystery knight at the tourney defends Howland’s honour by defeating three knights whose squires had bullied him the day before. The theory states, with more than sufficient evidence, that the mystery knight was Lyanna. Just like R+L=J, this theory is more or less confirmed, especially in the Season 6 Histories and Lore (see above).
3. F(Aegon), or the Mummer’s Dragon
(F)Aegon, or Fake Aegon is a theory that refers to Young Griff, or Aegon VI, the supposedly dead son of Rhaegar Targaryen. Though Jon Connington, the young prince’s ally and protector, claims Aegon to be a true Targaryen, events in the books suggest otherwise. AltShiftX lists all the evidence in his analysis of Varys’ actions and motives. Since the show’s excluded Aegon’s storyline, it’ll probably be a while before there’s more material supporting or contributing to this theory.
4. Ashford Tourney theory
First seen in a Tumblr post (see above), the Ashford Tourney theory is a just a tad less likely to come true than the other theories on this list. The theory is based on the tourney in The Hedge Knight, the first story in the Tales of Dunk and Egg series. The Ashford theory resurfaced later in an AltShiftX video in 2016, when Jon marrying either Sansa (his cousin) or Dany (his aunt) on the show seemed plausible. The theory compares the order of the five champions of the Ashford Tourney to the four (and the potential fifth) suitors os Sansa Stark. The theory’s strengthened by the fact that House Hardyng is on both lists, and that it isn’t a particularly prominent house. Again, this is a theory time (and the books) will tell, since the show sees major changes to Sansa’s storyline from season five onwards (like her marriage to Ramsay Bolton).
5. Dany’s womb can quicken again
In A Game of Thrones, the priestess Mirri Maz Duur tells Dany that she will never ‘bear a living child’ again. Not until ‘the sun rises in the west and sets in the east, the seas go dry and mountains blow in the wind like leaves.’ These conditions initially appear beyond the bounds of possibility, but by A Dance With Dragons, all three conditions have been fulfilled, in a way. The sun in the first part is Quentyn Martell, son of Doran Martell, whose sigil is a spear piercing a red sun. Quentyn journeys from Dorne in the west to Meereen in the east, and his death there symbolises the setting of the ‘sun’. The second part is satisfied when, in Dany’s final chapter in A Dance With Dragons, she describes the effect of the coming winter on the Dothraki Sea: “The grass was paler than she remembered, a wan and sickly green on the verge of going yellow. After that would come brown. The grass was dying.” And finally, Barristan Selmy’s chapter in ADWD describes the pyramids of Meereen collapsing into smoking ruins, which despite being a bit of stretch, could be ‘mountains blow(ing) in the wind’. Dany probably can bear children again, though this remains to be seen in The Winds of Winter.
In A Storm of Swords, Arya Stark leaves a dying Sandor Clegane under a tree by the Trident. In A Feast For Crows, Brienne of Tarth meets the mysterious Elder Brother of Quiet Isle, who tells her that the Hound died in his arms, and that he was now “at rest”. Theorists claim that the Hound ‘dying’ was metaphorical, and that Sandor Clegane is actually still alive. Gravedigger remains unconfirmed in the books (for now), but the show brought Sandor back in S06E07, albeit with a slightly changed storyline.
7. Frey Pie
Frey Pie is a more book-specific theory. In A Dance With Dragons, Wyman Manderly’s contribution to the wedding feast at Winterfell is three ginormous meat pies. It’s strongly implied that Manderly killed Rhaegar, Symond and Jared Frey and baked them into the pies. Frey Pie has tons of supporting evidence, so this poetic justice for the Red Wedding is widely assumed to be true. The show sort-of confirmed it, when Arya Stark presents Walder Frey with Frey Pie (though the Freys in question are Lothar and Black Walder) in S06E10.
Note: There are a lot more theories in ASOIAF than the ones on this list, and this post has links that takes you to more.