Fall Deadline (October).
From the Fulbright website: The Fulbright U.S. Student Program is the largest U.S. exchange program offering opportunities for students and young professionals to undertake international graduate study, advanced research, university teaching, and primary and secondary school teaching worldwide. The program currently awards approximately 1,900 grants annually in all fields of study, and operates in more than 140 countries worldwide. Competitiveness varies by world region (e.g., the UK is among the most competitive of regions).
There are several types of Fellowships, each typically for one year of study abroad:
For more information: http://us.fulbrightonline.org/about/fulbright-us-student-program