1. These theories are just my guesses with some text to back them up.
2. These theories will involve things that haven't happened in the show yet.
3. THIS POST CONTAINS SPOILERS. Read at your own risk.
Arya Stark, as well as the other Stark children, is gifted a direwolf. She names hers Nymeria after a warrior queen. When Sansa's direwolf is killed after the attack on Joffrey, Arya commands Nymeria to run away. Throughout the books, there are whispers of wolves attacking and Arya having warg dreams. Though it never states that Nymeria is the one responsible, I always assumed she was.
"The wolves have grown terrible of late. There are placces where a man alone would do well to find a tree to sleep in. In all my years the biggest pack I ever saw had fewer than a dozen wolves in it, but the great pack that prowls along the Trident now numbers in the hundreds."
"The say the pack is led by a monstrous she-wold, a stalking shadow grim and grey and huge. They will tell you that she has been known to bring aurochs down all by herself, that no trap nor snare can hold her, that she fears neither steel nor fire, slays any wolf that tries to mount her, and devours no other flesh but man."
Ser Robert Strong:
This hasn't happened in the show... yet. I don't know that they'll put it in there. At some point in A Dance with Dragons, Cersei demands trial by combat. She chooses Ser Robert Strong as her champion. He is never actually identified or described except his stature. The guy is huge. 8 feet tall and burly. He never takes his helmet off, so you never know who he is. I am going to postulate that he is either the legendary hero, Ser Clarence Crabb...
He was eight foot tall, and so strong he could uproot pine trees with one hand and chuck them half a mile. No horse could bear his weight, so he rode an aurochs....
His wife was a woods witch. Whenever Ser Clarence killed a man, he'd fetch his head back home and his wife would kiss it on the lips and bring it back t' life.
Kevan Lannister had a strong suspicion of just who this Ser Robert really was beneath that gleaming white armor. A suspicion that Mace Tyrell and Randyll Tarly no doubt shared. Whatever the face hidden behind Strong's helm, it must remain hidden for now. The silent giant was his niece's only hope.
Ice and Fire:
Since the series is called "A Song of Ice and Fire", I have some theories about how that is going to come into play.
At the very beginning, way back when Ned Stark was still alive (feels like ages ago, I know) the Starks had an ancestral blade of Valyrian steel. It was named Ice. When Ned Stark was beheaded for treason, Ser Ilyn Payne, the executioner, uses Ice to do the decapitating. After Ned's death, Ser Ilyn Payne carries Ice for awhile until Tywin Lannister takes it, has it melted down, and forged into two new swords, Widow's Wail and Oathkeeper.
There are two swords that potentially could be considered "Fire". Let's start with Blackfyre. Blackfyre was a Valyrian steel blade that was used by Aegon I. A Targaryen blade that has since been lost. Perhaps it will be recovered and some form of Ice and Blackfyre will meet up.
The other sword that could be fire is Lightbringer. As it currently stands, nobody is really sure if Lightbringer is real. It is supposed to be a weapon/tool of the Red God. Stannis' sword is claimed to be Lightbringer, but that has yet to be proven. So, for the swords, I think some form of Ice and one of these Fires will meet up at some point and the battle will be epic.
There are more obvious connections with these two. You have the White Walkers and the Dragons. This story may just end up not having anything to do with people at all. All the people will die, and the White Walkers and Dragons will battle it out.
This could be a house thing. Targaryens vs. Starks. It could be a reference to the Wall. There are a ton of options here. What are your theories about it?
I have a ton of other theories, but those are the big ones right now. I hope you enjoyed reading this and I will definitely post more as I come up with them.