While the Korean martial arts of Taekwondo is one of the most practiced martial arts in the world, there are many other lesser known styles in Korea, both ancient and modern. Korea has a long history of warfare, as well as cultural and military interactions with China, and styles such as Ssireum (Korean wrestling) and Taekkyon/Subak go back for thousands of years. Archery, swordsmanship and horse-riding are other arts which have a long history.
During modern times many martial arts have also grown up, many, such as Hapkido, Tangsoodo and Taekwondo have their roots in Japanese styles taught during the occupation of Korea. Others, such as Hwarangdo or Kicheon have questionable roots. A couple of good reads for some background on Taekkyon and Korean martial arts are Taekyon: The Korean Martial Art and 5,000 Years of Korean Martial Arts: The Heritage of the Hermit Kingdom Warriors.
Have a look at the above pages to learn more.