When we talk about the Seven Kingdoms, do we exclude the Riverlands, and therefore the Tullys are not a Great House, or the Iron Islands, and so exclude the Greyjoys? Just how many of these high lords are there?

The Seven Kingdoms were the Kingdoms of the North, the Mountain and Vale, the Isles and Rivers, the Stormlands, the Rock, the Reach, and Dorne. The Riverlands being under occupation by the Iron Islands at the time wasn’t counted as one of the seven, although historically there were Kings of the Rivers and Hills.

When Aegon conquered, he raised up the Tullys to the level of a Great House as reward for being the first to rally to his side against Harren the Black. So there are eight Great Houses: the Starks, Arryns, Tullys, Greyjoys, Lannisters, Tyrells, Baratheons, and Martells.