How many kings were there in The Seven Kingdoms at the end of season 2?

Answer 1

Four.

1. Joffrey Baratheon, the King on the Iron Throne
2. Robb Stark, the King in the North
3. Stannis Baratheon, the King in the Narrow Sea
4. Balon Greyjoy, the King of the Isles

After the death of Robert in Season 1, Joffrey ascended to the Iron Throne, and he remained king through Season 2. Robb Stark was crowned king by his bannermen at the end of Season 1 - he was King in the North, and the King of the Trident, through Season 2. Stannis Baratheon crowned himself in Dragonstone, as Robert’s rightful heir, and despite his defeat at the Blackwater in Season 2 Episode 9, was alive to stake his claim at a later date.

I don’t remember seeing Balon Greyjoy being crowned in the TV series, but when Theon took Winterfell (Season 2 Episode 6), he did mention that his father has donned the crown. With Robb in the south, and Moat Cailin fallen to the ironborn, Balon claimed kingship over not only the Iron Islands, but also the North.

Since the question asks only about the Seven Kingdoms, we can leave out Mance Rayder - the King beyond the Wall. Another king from Season 2 is Renly Baratheon, the King in Highgarden, but he didn’t make it to the end of the season, having been killed in Season 2 Episode 5.