The answer varies depending on which country you are from.
If you are a citizen of the United States and you are traveling to South Korea as a tourist, for less than 90 days, then you are not required to have a tourist visa. If you will be traveling for business, then you will need to obtain a work visa with sponsorship of a business in Korea.
If you are a citizen of a country other than the United States, then please visit http://www.visitkorea.or.kr/enu/GK/GK_EN_2_1_1.jsp, where you can view a list of requirements for each country. If your country requires one, then you may also apply for an extension in the case of an emergency or unforeseen circumstances.