Do you want rampant speculation? It's not a spoiler because it's just a theory...
Jon Snow is a Stark, but he's not Ned's son. He's the illegitimate son of the "mad king" and Ned's sister, making him half-Targaryan. Ned kept the boy's true lineage a secret - even from Catelyn - to protect his identity.
Dany has three dragons, and accordingly there will be three dragon riders, herself, Jon, and one character introduced in the fifth book and not yet in the TV series. With incest never being a problem for a Targaryan, Dany and Jon will marry to restore the Targaryan throne in the end - the series of books, after all, is a Song of Ice and Fire: Ice (Jon Snow) and Fire (Dany Targaryan) - as well as the white walkers (Ice) vs. the red priests (Fire). A nice duality.
Ooohhh...I like that theory!
I’d heard it rumored that one of the Targaryan children survived the rebelion though. Varys switched the baby of Martel’s sister and smuggled him to Essos. Which stands to reason why Varys was colluding with Iliryo to wed Dany to Khal.
A surviving Targaryn would dispute Dany’s claim to the throne.