In which Targaryens are featured? Game of Thrones?

In addition to Daenerys and Viserys, Aemon Targaryen (Peter Vaughan() was used throughout the series. Known as the last known Targaryen in Westeros, he was the great-uncle of Daenerys and Viserys. 

It is revealed in the finale of season seven that Jon Snow (Kit Harington) father is Rhaegar Targaryen (Wilf Scolding) and that his birth name is Aegon VII Targaryen, making him the heir to the Iron Throne and Daenerys’ cousin. 

Why are the House Targaryen families so closely linked?

Simply put, they loved to wed.

According to Game of ThronesThe family was known for marrying multiple siblings to preserve the bloodline. 

The desire to be pure led to some issues later on, with the possibility of genetic problems, or inbreeding, sometimes resulting from the crossing. “Madness and greatness are two sides of the same coin,” Lord Varys (Conleth Hill“The Targaryens from season eight” was what he said. “Every Targaryen born is a chance for the gods and world to watch how the coin lands.”