Probably depends on where you live.
I think the only worldwide popular is the British Royal Family.
In Italy and France, Spanish and Belgium are quite popular, also Monaco and Savoy dynasty.
In others country, expecially the Northern Europe only Danish, Swedish, Belgium and Spanish.
Liechtenstein, Netherlands Luxembourg and Japan are not popular in Italy.
For not reigning royal family only Savoy dynasty is very popular in Italy, quite Borbone of Two Sicily, Romanov and House of Habsburg and Bourbon of France, but more for the past than today.
In France for example only Bourbon of France and Savoy dynasty are popular for the not reigning houses.
Aga Khan dynasty are popular in the past in Italy, today not so much. Only the name Aga Khan is popular and also Rita Hayworth, but the actual members of the family are not popular in Italy.