[nerd]^ Elaborating on that, I was perusing wiki, and it looks like Robert/Stannis/Renly's grandmother was a Targaryen (and the niece of Maester Aemon.) Likewise, Aemon would be the great grand uncle of Daenerys (as his brother was Aegon V, her great grandfather.)
Yep.
The Baratheons were also founded by an alleged Targaryen bastard, and the only one of the great houses to date to Aegon's conquest.
So, just a reminder, particularly for you non-book readers:
The Starks, Lannisters, Arryns and Martells were all once royal houses, when the Seven Kingdoms really
were Seven Kingdoms. The Starks are the oldest of these lineages, having ruled the North for over a thousand years.
The other royal houses were ended by the Targaryen invasion, and their land is now controlled by houses that used to serve as bannermen to those kings - the Tullys in the Riverlands, and the Tyrells in Highgarden.
The Greyjoys are a special case as they're the family appointed to the Iron Islands by the Targaryens but are also descended from the Grey Kings.
This leaves the Targaryens and the Baratheons as the only 'new' great houses in Westeros, dating after the conquest. The founder of the house slew the King of the Storm Lands, and since then the Baratheons have been Lords of Storm's End, a keep like Winterfell for the Starks or the Eyrie for the Arryns.
Renly Baratheon is the current Lord of Storm's End, while Stannis Baratheon is the Lord of Dragonstone, which is former Targaryen territory.
HOWEVER.... it looks like the show decided to skip over a generation (Jaehaerys II), as Aemon says that "Mad King" Aerys II was the son of his brother, Aegon V, not the grandson, making Aemon Daenerys' grand uncle, not great grand uncle.[/nerd]
Wow, that completely slipped me by.