General term for royalty:
* Rodzina królewska (royal family)
Specific terms for members of royalty:
* Król (king)
* Królowa (queen)
* Książę (prince)
* Księżna (princess)
* Królewicz (prince, son of a king)
* Królewna (princess, daughter of a king)
The most accurate translation will depend on the specific member of royalty you are referring to.