Below are the most common family names that make up over half of the Korean population  (http://www.korea.net/koreanculture/artsandculture/names):
Family names that came from the Chinese immigrants in the Three Kingdom Period (1st-3rd centuries A.D.) include Cho, Hwang, O, Ryu and Yi. However, later some Koreans also adopted these family names.
The Goguryeo Kingdom, which had contact with China first, had family names such as Ko and Myeongnim. The Baekje[?] Kingdom had an aristocracy with the names Baek (Paek), Guk (Kuk), Hyeop, Jin (Chin), Sa, and Yeon. Silla[?] Kingdom had royal names such as Bak (Pak), Gim (Kim), and Seok.
The ancient kings of Korea gave their subjects family names. For example, in 33 A.D., King Yuri gave tribes of Saro (Silla) names like Bae (Pae), Choe (Ch'oe), Jeong (Chŏng), Son and Seol (Sŏl). Other names given by kings are An, Cha, Han, Hong, Kim, Kweon, Nam, Eo (Ŏ), and Wang.
Under the Japanese occupation of the 1940s, Koreans were "suggested" to take Japanese family and given names. This is called "Name Order" (創氏改名). Over 83 per cent of the population (25,133,352)  conformed (at least temporarily) to this Japanese regulation.
 Figure from Andrew C. Nahm, Korea: Tradition and Transformation. (1988) Page 233.