Jon Snow and Daenerys Targaryen shouldn’t be a 'ship that works, and yet, somehow, I can’t keep myself from hoping those two crazy kids get together before Game Of Thrones ends. Not only will they be able to continue the Targaryen line in the tradition of their ancestors — specifically, by getting hitched to relatives — but she’s the ice and he’s the fire! If they did ascend to the Iron Throne together, though, would Daenerys and Jon Snow be able to have kids to take over when they die? Or would their family end with the two of them?
Based on what she told both Tyrion Lannister and Jon Snow, Daenerys is pretty convinced that she will not be able to produce heirs and that her dragons will serve as her only living children. Longtime fans know that this isn't Daenerys refusing to have kids; rather, she believes that she is physically infertile. This goes back to Season 1, when she actually was pregnant and enlisted the help of Mirri Maz Duur, an enslaved priestess, to heal her husband Khal Drogo with blood magic. Not only did she put Drogo in a coma, but she took Daenerys’ unborn child as the blood payment, causing her to have a miscarriage. When Daenerys asked her when Drogo would wake up, she responded:
"When the sun rises in the west and sets in the east. When the seas go dry and mountains blow in the wind like leaves. When your womb quickens again, and you bear a living child. Then he will return, and not before."
Whether or not Mirri Maz Duur's prophecy is true is another matter altogether; if it's not, however, it's very likely to say that Jon and Daenerys will accidentally end up with a kid, because boy were they making goo-goo eyes at each other at the end of this episode. There's no way these two aren't getting together at some point, and it's not as if birth control is all that sophisticated in Westeros. I've had good enough sex education to know that if you go at it for long enough without protection, the odds are you're going to end up pregnant at some point.
If Daenerys truly is infertile, however, then there are certainly other ways of finding a successor, if that's what Jon and Dany care about. Jon is a Targaryen too, after all, and as Gilly learned last week, his parents were wed in secret, meaning he also has a legitimate claim to the throne. He could father a child with another woman and legitimize them to be his heirs, which only a king is able to do. Sure, it wouldn't be Dany's kid, but they would still technically be related by blood, and Targaryen heirs have wed outside of their family for political reasons in the past. Heck, before Rhaegar Targaryen was Jon Snow's dad, he was married to a Martell, not another Targaryen. His first group of children would have only been half-Targaryen, too, and they still would have been eligable for the throne, exactly the way that Jon Snow is now.
However, is that what either of them wants? Daenerys knows that she must find an heir eventually, but she definitely doesn't seem to want to talk about it, at least not with Tyrion. And even though she's clearly attracted enough to Jon Snow to test the waters regarding his thoughts on children, he's always been a bit squeamish about the possibility of having a kid — remember, he was a virgin when he got to the Wall because he hated growing up a bastard and didn't want to inflict that on anyone else. He took an oath to father no children, and even though his watch has ended, he still might not be up for it.
But like Daenerys said (in so many words), that's a bridge for them to cross when they come to it. First, she and Jon have to convince Cersei to chill out for a minute, stop the Night King's army, and start hooking up with each other on Game of Thrones before kids even enter into the equation. That's a much longer to-do list then most would-be parents have.