The government of Spain offers through different official institutions grant opportunities in all academic areas to American students wishing to pursue a graduate degree, doctoral dissertation or research in Spain. Existing opportunities include:

Scholarships for graduate and doctoral students and researchers in Spain from the Spanish Agency for International Cooperation for Development of the Ministry of Foreign Affairs and Cooperation.
Becas del Ministerio de Educación, Cultura y Deporte
Scholarships from the Ministry of Culture.
The Fulbright Commission for cultural, educational and scientific exchange between the USA and Spain offers grants in a wide variety of fields.