So, I was catching up on the second season of Game of Thrones and something just kinda hit me. I'm going to put this in spoiler tags, although it's purely conjecture and I don't think it actually spoils anything past the first or second book. Nevertheless, whatever.
There's only really a few events in the series that are shrouded in complete mystery. Well, aside from The Others in general and the 'Doom of old Valaria" or whatever. But The Others is kind of just a mystery to everyone - they're just there, they're coming back, and they kill shit. Old Valaria is a minor background point.
As far as the main characters and key plot events, I can only really think of three major things that I consistently wondered about while reading the books. One I won't be mentioning as it's a pretty big spoiler for book 3 or 4, but the other two are implied right at the beginning and haven't been brought up much since. Which kinda makes me think that they're pretty important.
1.) John Snow's mother. It was kinda drilled into our heads that Eddard wouldn't talk about it and no one really knew for sure, even Robert. I've been curious about this but also thought it was just a good way to dismiss the issue - it doesn't matter it just served to give the Stark's a bastard and also show that Eddard had his faults. I'm not so sure about that anymore.
2.) This is kind of two in one but the events at "The Tower". During the first book, Eddard has a series of flashbacks revolving around arriving at some tower with his companions right after or at the very end of the war. The remaining members of the Kingsguard are there. Battle breaks out, Stark and his awesome swamp dwelling friend are the only guys left standing. The significance of these flashbacks hasn't been shown yet, but it seems pretty obvious that there is some importance to the scene. The second part is that "The Tower" (I totally can't remember the name of it) is where Lyanna Stark was when Eddard found her (I assume why he was there in the first place) and where she died. But more importantly, where she made him promise her something. Something that hasn't been revealed but seems to be pretty significant. Especially since, with the death of Ned Stark, the revelation of the existance of said promise kind of shows that it's more important to the overall story arch than it is just an aspect of character development or motivation for Ned.
I'm starting to think that Lyanna Stark is John Snow's brother by way of Rhaegar. Dude may have kidnapped her, but the general feel of the story is that she kind of eloped as well. I had wondered exactly what killed her, especially at so convenient a time, and childbirth kinda makes sense - she was at the tower with child...royal child and thus the presence of the Kingsguard. And Eddard, a retardedly noble and honour bound man comes back with a baby immediately after. It pretty conveniently wraps up the questions of the events of the tower, the promise, and John Snow's mother in one easy (maybe too easy) answer.
Aaaaand, I just googled it and it seems that this is a pretty popular theory. Interesting to see where it goes, at least.