The death of Robert Baratheon, and his goring by the boar that lead to it (both offscreen) caught me totally off-guard. It seemed at the time like this terrible thing he didn't deserve, and landed everything in utter turmoil. I hadn't read the books at that point, and expected it really was mostly this "whodunit" with a bit of the supernatural sprinkled in.
I watched the first two seasons of the show barely understanding what was going on, wondering if Dany's experiences in Essos (not that I knew it was called that) would ever cross over in any significant way in Westeros. Then I finally understood all of the relationships, why this white-haired chick was trying to get back to her home (which I originally thought was Valyria and NOT Westeros), why Ned's death -- while horrifying -- was an event that really drove the narrative in ways I couldn't appreciate when the loss was still so raw.
So, in looking back, I found the subtext. I re-watched the scenes between Robert and Cersei, and the implication that she had him poisoned really was there all along. Robert's poor treatment of Lancel and the fact that he was the one who always fetched the wine. Or that Lancel and Cersei were getting it on in Season 2. (I barely realized he was the same guy.) It all clicked in a way it never had on the first viewing.
I won't say nothing ever comes out of nowhere, but I gained an appreciation for the slow burn of the plot, and eagerly anticipate watching this season again (and perhaps earlier) once it's all over in a couple of weeks.