Currently, there are no required or specific vaccinations for travel to South Korea.
It is highly recommended that all travelers to any part of the world, including Asia, be up to date with routine vaccinations such as Hepatitis A, Hepatitis B, Measles-mumps-rubella, Tetanus, and Typhoid. If you have any questions about health, be sure to contact your doctor prior to departure.
Hospitals, such as the Samsung Medical Center, and doctors in the county are some of the best in the world if you have any issues or need medical help while abroad. Setting appointments with doctors is usually hassle free for foreign visitors and costs are relatively low compared to the United States and other countries.
If you would like to see up to date information, you can visit the CDC website at http://www.cdc.gov/travel/destinations/south-korea.htm for more information.