I guess you mean the UK's royal family, in which case I'll also say the late QE II. Otherwise I'll also join Splashee and go for Carl Gustaf, since he is incredibly down-to-earth by royal standards and has (in my opinion*) handled the transition to an increasingly anti-monarchic society quite well in Sweden, and ironically retained a great deal of his popularity due to that.
*I'm not a Swede and have only ever lived in Sweden for 11 months and visited twice more, so my opinion is essentially meaningless, but hey-ho.