Options for undergraduates:
Korea America Student Conference (so awesome it is hard to explain in a single phrase, but essentially a month-long intensive cultural boot-camp ^^)
NSEP Boren Undergraduate Scholarship (for a summer or full-year of study abroad)
Freeman-Asia (for a summer or full-year of study abroad)
TALK and EPIC Programs (teaching English in Korea for one year, fully funded by South Korea; TALK is for currently enrolled undergraduates and EPIK is for graduates who already have a BA)
Options for graduates and undergraduates entering their senior year:
Flagship Language Program (fully funded, two years of intensive language study, spread between the University of Hawaii and Korea University)
Fulbright Full Grant or English Teaching Assistantships (ETA) (fully funded; graduating seniors and graduate students can apply to spend a year abroad in Korea either doing independent research or teaching English)
Graduate Study in Korea (numerous fully and partially funded opportunities for studying an MA in International Studies or many other fields at a university in South Korea ~ this can be a good step towards jobs in the foreign service, K-Studies PhD back in the states, doing business in Korea, etc.)
Refer to my earlier blog entry about scholarships and programs for Graduate Schools of International Studies in Korea.