Who is the Prime Minister of Spain?

No one; Spain does not have a Prime Minister. The constitutional title for the Head of the Spanish government is "Presidente del Gobierno" (President of the Government), even though it is exactly the same role as Prime Miniser and functions in exactly the same way.

Mariano Rajoy Brey is the current Presidente del Gobierno and was inaugurated on December 21, 2011. Rajoy was born March 27, 1955, graduated from the University of Santiago de Compostelo, and is a member of the Peoples Party.

They also have a king named Juan Carlos I. The king is the Head of State.