There's loads of foreshadowing throughout every season ... some are a little bit of a stretch but this is fantasy and the fandom will go to any lengths.
SPOILERS AHEAD FOR VARIOUS SEASONS - YOU HAVE BEEN WARNED
● Ned’s death is foreshadowed in episode one -
In the very first episode of the series, Ned, Jon, Theon, Robb and Bran find a dead direwolf. We find out that this direwolf (House Stark sigil) was killed by a stag (House Baratheon sigil) and has a pair of antlers in its neck - foreshadowing Ned's beheading at the order of Joffrey at the end of the season.
● Jaime says he couldn't live with being crippled -
In the second episode of Season 1 Jaime is talking about Bran and says to Tyrion, “Even if the boy lives, he’d be a cripple. Grotesque. Give me a good, clean death any day.” Rewatching it's quite obviously meant to foreshadow later events. But when this episode aired, it just seemed like a throwaway line.
● Bran’s Warging abilities - they are heavily hinted at from season 1; Bran has lots of visions of running around as a wolf, though it seems like these are just the dreams of a crippled child who used to run free but is now stuck in his bed. There’s also the scene at the very end of the second episode of the series when Ned has to kill Lady (Sansa's direwolf) and we cut from the direwolf dying to Bran waking up.
● Bran predicts Arya's revenge on Frey - in season 3 Bran tells Hodor and the Reeds a story about a Night's Watchman who got revenge by killing a king's son, baking him into a pie, and feeding it to the king. Fast forward 3 seasons and in season 6, Arya kills and bakes Walder Frey's sons into a pie, and feeds them to him without his knowledge, avenging her own family's death.
● Theon's captor in season 3 - we don't know who it is for the most part but it was foreshadowed when Theon is being chased by a group of Bolton's who are all stopped and killed by one lone man. One Bolton in particular looks up at Ramsay and says "you little bastard" right before he dies. Not only does this imply that he recognises Ramsay, but the phrase "little bastard" obviously has a double meaning here. Just from that, we could easily figure out that this is a Bolton and a bastard son, yet the line appeared to be just another gratuitous use of a swear word.
● Another one for Theon, where he predicted his own downfall - in season 2 he's looking for the Stark boys and he's worried he'll be humiliated for not even being capable of stopping a crippled child escaping him. He grabs Maester Luwin and says, "I'm looking at spending the rest of my life being treated like a fool and a eunuch by my own people!" Truer words have never been spoken by someone about to lose their genitals in a few episodes time ...
● The death of Dany's child - Mirri Maz Duur tells Dany that only death can pay for life when she is trying to save Drogo. In one scene Dany asks, "My death?" Mirri responds, "No. Not your death, Khaleesi." Right after she says that, for just a second, Mirri's eyes shift and she looks directly at Dany's stomach. This hints at the fact that it's Dany's child who will die in payment, as seen at the end of the season.
● Littlefinger is good at predicting deaths - In season 4 Littlefinger is talking to Robin Arryn and says "People die at their dinner tables. They die in their beds. They die squatting over their chamber pots." Subsequently Joffrey was poisoned at his dinner table, Shae was strangled in bed, and Tywin was shot while sitting on the toilet.
● Again with Littlefinger foreshadowing death, this time his own - in Season 1, Littlefinger holds a dagger to Ned Stark's throat and says, "I did warn you not to trust me." By doing this Littlefinger is also foreshadowing his own death. He threatens Ned in the great hall of King's Landing, and ends up having his throat slit by Arya Stark in the great hall of Winterfell after he trusted Sansa to betray her sister.
●Melisandre predicting Arya's future - in season 3, Arya Stark meets Melisandre who grabs her and looks into her eyes, telling her what she sees there: darkness and eyes of all different colors, "eyes that [Arya] will shut forever." This has multiple layers of foreshadowing as Arya will go on to become a Faceless Man and take on others' appearances to kill lots of people, shutting their eyes forever.
● Margaery predicts her Sparrow torture - Margaery Tyrell jokes she'll end up with a "string of sparrows" around her neck if Joffrey has any say in her jewellery for their wedding. Later on, the religious fundamentalist Sparrows imprison her and torture her for her involvement with the Lannisters and she ends up dying surrounded by Sparrows in the Sept of Baelor.
●Sam predicting Jon's return - when Olly was worried about Jon being Beyond the Wall Sam reassures him by saying "I've been worrying about Jon for years. He always comes back." Jon is later stabbed by Olly, only to come back to life as Sam warned he would.
● The Lannisters taking power from the Baratheons - in the seventh episode of Season 1, King Robert is killed in a "hunting accident" which left his "son" Joffery as the new ruler. In the same episode Lord Tywin is shown skinning a stag (the Baratheon sigil). This is blatant foreshadowing of the Lannister's takeover of the Iron Throne by stripping the power from the Baratheons.
●The Red Wedding - there are so many foreshadowing moments for this:
• In "The Pointy End" where Walder Frey is brought up for the first time. Catelyn says about him "Some men take their oaths more seriously than others,"
And why does the Red Wedding happen? Because Robb Stark swore an oath to marry one of Walder Frey's daughters and then married Talisa instead.
• In Season 2, Varys and Tyrion Lannister talk about how they hate the city bells. Varys says, "I've always hated the bells. They ring for horror. A dead king. The city under siege." Tyrion adds, "A wedding."
• Also, when the Hound had Arya and was taking her to the Twins in Storm, intending to return her to her family in hopes of either a reward or being allowed to pledge allegiance to the Starks he tells Arya, "Keep your mouth shut and do as I tell you, and maybe we’ll even be in time for your uncle’s bloody wedding.”
■ Jon Snow is a Targaryen- this has been hinted and foreshadowed in many ways from season one:
▪ "King Jon of the Andals" - In episode 1, when Ned Stark is about to behead a deserter, he says a few words. The camera pans to Jon just as he says the 'King of the Andals' bit. It may just be coincidence, or it may be a prediction of Jon's royal future.
▪ Aemon predicts Jon Snow being a Targaryen -
When Aemon is talking about Daenerys to Sam, he says, "A Targaryen alone in the world. It's a terrible thing." The camera pans immediately to Jon as soon as he says this, predicting Jon's own lineage.
▪Ned Stark purposefully didn't call Jon Snow his son. When Jon asked Ned about his mother on season one, Ned replies: "You are a Stark. You might not have my name, but you have my blood." The Stark family blood does indeed run through Jon. It just happens to be Lyanna's blood, not Ned's.
▪Rhaegar puts Jon's protection above his own to save him even knowing he'd probably die- In the first Tower of Joy vision in season six, young Ned and two Targaryen Kingsguard have a confrontation:
"Rhaegar lies beneath the ground. Why weren't you there to protect your prince?" Ned asks.
"Our prince wanted us here," Ser Arthur Dayne replied.
This is big deal, because the five Kingsguard are sworn to protect the royal family at all costs. Rhaegar's choice to station two of his five protectors at the Tower of Joy must mean there is something significant inside he wants safe, and what is more important than his heir?