Rob Bricken writes:

If there's two things fans of the A Song of Ice and Fire book series can agree on, it's that 1) author George R.R. Martin is weaving an incredibly dense tale where far more happens (and has happened) than what's just on the page, and 2) that no character is safe from GRRM's murderous pen. In regards to the former, fans have spent the last 17 years since A Game of Thrones was first published reading between the lines, trying to figure out the series' many, many mysteries. One astute fan by the name of Full-Faced Braavosi took the time to compile all the theories, both likely and insane, over at the mega-fansite Westeros.org; we thought we'd take the chance to make sure all you ASoIaF readers are caught up on every fan theory you absolutely need to know.

More: http://io9.com/5979065/all-the-game-of-thrones-fan-theories-you-absolutely-need-to-know

I include my favorites below...

Is Syrio Forel Alive?

Everyone wants Syrio Forel, Arya's awesome "dancing instructor" from A Game of Thrones, to be alive. That's how awesome he is. In truth, he doesn't die "on page," so to speak — he sends Arya away, and takes on the armed Lannister guards sent to capture Arya with a wooden training sword. It's dire, but Syrio is the First Sword of Braavos, so it's not completely unreasonable to imagine he still beat the guards, and then went on his merry way. But given that Syrio is Braavosi, and Arya's next adult friend is the Braavosi assassin Jaqen H'ghar, who takes an odd interest in Arya and who can also magically change his face, a lot of people think Jaqen might have been Syrio, still watching over his charge. This would indicate a very early interest in Arya by the Faceless Men, the highly skilled league of assassins that Arya has ended up with, but for no known reason. Still, such is the awesomeness of Syrio. (For more, continue reading here.)

Is Syrio the Faceless man?

http://reddit.com/r/gameofthrones/comments/24vk7e/show_spoilerstheory_the_hound_reminded_me_of_a/

Conclusion: He's not Jhaqen H'agar.

To be a dancing master is one thing, to be a faceless man is another thing entirely. Jhaqen H'agar

Their philosophies also seem kinda contradictory - "What do we say to the God of Death? Not today" vs "All men must die."

More theory Syrio is alive:

http://pandawhale.com/post/43343/the-hounds-quote-in-s4e5-about-armor-and-syrio-forells-wooden-sword-bugged-me

Syrio Forel's main value was in training Arya's mind:

http://reddit.com/r/gameofthrones/comments/2lo24i/season_1how_much_did_arya_learn_from_syrio/

Not today.

http://pandawhale.com/post/43437/syrio-forel-not-today-gif

I think he's alive. In season 4 ep 5 where Arya and The Hound were talking about Syrio being killed by Meryn Trant, The Hound's voice sounds surprised and laughed it off. He even told her, "The greatest swordsman ever lived killed by Meryn Fucking Trant." and "any boy whore with a sword could beat three Meryn Trants." This may justify that Syrio is still alive. We all know The Hound is also a good fighter and he knows in King's Landing whose soldier is good or not. He knows Meryn Trant is just a douche and a water dancer and 'The First Sealord of Braavos' like Syrio Forel wouldn't just be killed like that even he's outnumbered.

That's a good theory! I hope you're right. 

With Arya in Braavos this year there's a good opportunity to surprise us with his return.

I've also heard a theory that Syrio Forel is Jaqen H'ghar, who watched over Arya until she was safe. 

Another connection:

http://pandawhale.com/post/71704/another-connection-between-syrio-forel-and-jaqen-hghar

What Is Jaqen H'ghar Doing?

When Jaqen leaves Arya (with the Braavosi coin and the phrase "valar morghuli," which eventually brings her to Braavos and the Faceless Men), that's not the last we see of him. It is undoubtedly Jaqen in the prologue to A Feast for Crows, who –- in the guise of the Alchemist, the face Arya saw him change into –- murders the novice Pate at the Citadel… the same Citadel where Sam Tarly has gone to become a Maester and research the Others… and who meets the same Pate, alive and well. So Jaqen is definitely at the Citadel. Seeing as the Citadel is the most learned place in the world, it seem Jaqen is trying to learn something… or prevent someone else from learning something. The real question is if he's working for someone specific, or on behalf of all the Faceless Men? (For more, continue reading here.)

Might Tyrion Lannister Actually Be a Targaryen?

We all know "dragons" equal "Targaryens" in A Song of Ice and Fire. Daenerys is already a Targaryen, and as per above, most people think Jon is, too. So what about Tyrion? Some readers believe that the Mad King Aerys is Tyrion's real father, having forced himself on Tywin's wife Joanna, with Tywin never knowing, or possibly even being a willing pimp. GRRM mentions at one point that Aerys definitely found Joanna attractive. Jon describes Tyrion as having hair so blonde as to be white, which sounds a lot more like Targaryen's hair color than the Lannister blonde; plus, Tyrion has one green eye (very Lannister) and one black eye… and Daenerys' eye color is described as to be so purple it's practically black. Last but not least, Tywin himself tells Tyrion he's "no son of mine," although admittedly, that's immediately after Tyrion shoots him with a crossbow, so perhaps he was just being shitty.

The biggest reason for this theory seems to be Tyrion's prominence in the story, which equals Jon Snow and Daenerys, making them the three primary protagonists. Tyrion being a secret Targaryen would easily explain why GRRM has followed his story so closely, even when he flees King's Landing at the end of A Storm of Swords, and essentially leaves the "Game" for quite some time. Besides, the next most obvious Targaryen candidate is Aegon (more on him below), who only showed up in the most recent book, and has had no point-of-view chapters.

On the other hand, someone claiming Aerys found Joanna hot is hardly proof he took her for her own. And Tyrion being a Targaryen would negate all the wonderful issues he's had with his father and Lannister siblings, and that would be an enormous waste. (For more, continue reading here.)

Who Are Jon Snow's Parents?

It's the question all A Song of Ice and Firereaders ask themselves in book one, and never stop asking. The most prevalent theory is that Prince Rhaegar Targaryen, who abducted Eddard's siter Lyanna and the love of Robert Baratheon's life and inadvertently started the rebellion that deposed the Targaryens, had sex with Lyanna –- maybe consensually, maybe not –- and Lyanna died giving birth to Jon. Knowing that Jon would be in considerable danger if his half-Targaryen blood were revealed (remember, Robert was determined to kill every last Targaryen on the planet), he pretended the boy was his own bastard, and took him to Winterfell, telling nobody the truth. Although Ned is incredibly secretive regarding Jon's parentage, he does remember making Lyanna a promise on her death bed, which was likely to keep Jon secret and safe.

Jon's parentage seems likely to most readers – so likely, in fact, that some people believe it's too obvious to be true. Other fans have theorized that Jon is genuinely Ned's child, possibly with some random woman, or possibly with Ashara Dayne, whom Ned was rumored to love. The question is whether Ned's honor is great enough to have precluded him from fathering a bastard — certainly Catelyn and Ned's friends were shocked at the idea Ned had cheated –- and as shown in GoT, Ned is honorable to a fault. So it seems unlikely, although if he did lapse, his shame might be the reason he's so quiet about Jon's parentage. But if his mother is Ashara Dayne or some random wench, that doesn't really explain why he wouldn't at least tell Jon.

Certainly, George R.R. Martin loves his head games, but the idea that Rhaegar and Lyanna are Jon's true parents makes the most narrative sense. And it seems unlikely that Martin would be hinting at the mystery so much only to reveal Jon is just Ned's regular ol' bastard. (For more details and theories continue reading here.)

What Was the Real Reason for Robert's Rebellion?

There's no real easy way to summarize the amazing fan theory usually referred to as "Southron Ambitions," but the simplest version is that there was a lot more going on in Westeros before Rhaegar kidnapped Lyanna Stark and kickstarted Robert's Rebellion. In fact, Rickard Stark, Ned's father, may have had a grand plan to unite the kingdoms against the Targaryen rule on his own, creating relationships with House Tully Baratheon, Arryn, and even House Lannister in preparation for this war. It all went to hell when Rhaegar stole Lyanna and Aerys burned Rickard and Ned's brother Brandon alive, but seriously, read this admittedly lengthy theory here, and prepare to have your mind blown.

What Is Varys' Deal?

We all know what Littlefinger wants –- power. But what about the eunuch Varys? He does at least as much political maneuvering as Littlefinger, but his intentions are not nearly so clear. He tells the imprisoned Ned that he's trying to help the people of Westeros, which is a situation he definitely didn't need to lie in. But if he's telling the truth, how does he plan to help the people?

Arya hears him plotting with Illyrio Mopatis in GoT, planning for the Targaryen-led Khals to attack while Westeros is already at war., and the possibility of needing to kill Ned. And Illyrio is the one who wed Daenerys with Khal Drogo, theoretically giving Viserys a cavalry of barbarians (we all know ho that worked out, but still). He also helped warn Daenerys that Robert had sent assassins after her. More importantly, Varys is reportedly the person who apparently spirited Prince Rhaegar's infant son Aegon VI out of Westeros to be raised by Illyrio. It seems quite obvious that Varys is a Targaryen supporter, albeit one that realized King Aerys was too mad to rule. The real question is whether Varys truly puts the smallfolk ahead of Targaryen rule –- and if it comes down to Aegon or Daenerys, who would he pick? (For more, continue reading here.)

As of Game of Thrones season 4, episode 5, we know that Littlefinger REALLY wants power:

http://pandawhale.com/post/42963/littlefingers-grand-plan-an-in-depth-look-at-the-events-leading-up-to-the-s4e5-jon-arryn-reveal-chaos-isnt-a-pit

http://pandawhale.com/post/42839/game-of-thrones-season-4-episode-5-first-of-his-name-gifs-and-memes

But it's still unclear what Varys wants. See for example this scene from season 1, episode 5:

http://pandawhale.com/post/42849/arya-stark-chasing-cats-overhears-varys-talking-about-daenerys-in-s1e5

Updated for season 5:

http://pandawhale.com/post/60796/all-the-game-of-thrones-fan-theories-from-io9-you-absolutely-need-to-know-after-5-books-and-4-seasons-spoilers