For being such a tiny country Korea has a seriously impressive list of martial arts, far more than most other large countries.
It is true that they have been at war for almost their entire history and still today which must be one of the main reasons they have developed so many fighting styles.
During various invasions it was illegal for them to practice many forms, though they were still handed down in secret.
The Koreans have earned a reputation for fighting off significant attacks from larger better equipped armies - a trait they still clearly cling to today.
What is also amazing compared to other countries is that these arts use a wide range of styles from wrestling based styles to those like Taekwondo featuring acrobatic kicks where as other countries may be known for just one core type of fighting.
And even more notable is that several of these Korean martial arts have spread across the globe and built up followings matching or surpassing any other one style.
These arts involve incredibly well developed empty hand techniques as well as a huge range of weapons.
In recent years there has also been a big revival of other Korean fighting arts including sword arts, knife fighting and archery.
The Korean martial arts are also well known for philosophy and moral codes.
An example of the principals from one of these styles is as follows:

• Loyalty to one's king.
  
• Respect to one's parents.
  
• Faithfulness to one's friends.
  
• Courage in battle.
  
• Justice in killing.
  

Still today there is much controversy over the origins of some of these martial arts, with the Japanese claiming the basics originated in Japan, while of the Koreans obviously claim the opposite is true.
Regardless it is still an impressive list, check out the list according to Wikipedia: Korean martial arts:

1. Choi Kwang-Do
2. Chung Suk Kuhapdo
3. GongKwon Yusul
4. Gwonbeop
5. Gwon-gyokdo
6. Gyongdang
7. Haidong Gumdo
8. Han Mu Do
9. Hankido
10. Hapkido
11. Hoi Jeon Moo Sool
12. Hwa Rang Do
13. Kuk Sool Won
14. Kumdo
15. Kung Jung Mu Sul
16. Muye24gi
17. Shippalgi
18. Ssireum
19. Subak
20. Sul Ki Do
21. Taekkyeon
22. Taekwondo
23. Tang soo do
24. Yusul