If you are yet to watch season 7 of Game of Thrones and would hate to be told anything that has happened or been mentioned, then please do not read this post. This is something I noticed based on what has been said as well as fan theories about parentage of characters.
Spoiler bit
It has been confirmed that Jon Snow is in fact Aegon Targaryen and it has been theorised by many that Tyrion Lannister is also a Targaryen (Tywin said he couldn't prove that Tyrion is or isn't his biological son).
Danaerys' Targaryen - Mother died after childbirth
Jon Snow/Aegon Targaryen - Mother died after childbirth
Tyrion Lannister (possibly son of Mad King) - Mother died after childbirth
I found it interesting that the three of them, two definite Targaryens and the third a possible (his own father admitted he cannot know for sure Tyrion is his own son) all had been born and their Mother died as a result. Clearly there is a problem in the Targaryen line. It made it seem to me that Tyrion is a Targaryen. Just thought I'd share this with you.