Korean era names were used during the period of Silla, Goguryeo, Balhae, Taebong, Goryeo, Joseon, and the Korean Empire. Dangun-giwon, the era name originating from the foundation of Gojoseon is also widely used in Korea as an indication of long civilisation of Korea. 
List of Korean era names
Goguryeo Yeongnak (, "Eternal Happiness" : 391-413, during the reign of King Gwanggaeto the Great.) Note: The following era names are found on various Goguryeo artifacts, but the actual years of usage are unclear.
Yeonsu (, "Enduring Life" : 413 - 491 during the reign of King Jangsu or 270 - 292, during the reign of King Seocheon or 331 - 371, during the reign of King Gogugwon.)
Yeon-ga (, "Enduring Excellence": 292 - 300, during the reign of King Bongsang or 531 - 545, during the reign of King Anwon.)
Geonheung (, "Establishment of Prosperity" : 413 - 491, during the reign of King Jangsu.) Yeonggang (, "Eternal Peace": 545 - 559, during the reign of King Yangwon.)
Geon-won (, "First Establishment" : 536 - 551), during the reign of King Beopheung and King Jinheung)
Gaeguk (, "Opening of the Country" : 551 - 567), during the reign of King Jinheung)
Daechang (, "Great Light": 568 - 572), during the reign of King Jinheung)
Hongje (, "Vast Relief" : 572 - 583), during the reign of King Jinheung, King Jinji and King Jinpyeong)
Geonbok (, "Establishment of Blessings" : 584 - 634), during the reign of King Jinpyeong and Queen Seondeok)
Inpyeong (, "Even Benevolence" : 634 - 647, during the reign of Queen Seondeok) Taehwa (, "Great Harmony": 647 - 650, during the reign of Queen Jindeok) In 650, Silla stopped using its own era names and adopted those of Tang China. Gyeong-un (, "Clouds of Celebration": 822 during the reign of Kim Heonchang's Jang-an state.)
Cheontong (, "Authority of Heaven": 699 - 718, during the reign of King Go.)
Inan (, "Benevolence and Good": 719 - 736, during the reign of King Mu.)
Daeheung (, "Great Prosperity": 737 - 793, during the reign of King Mun.)
Boryeok (, "Precious Era": 774-?, at least until 781, during the reign of King Mun)
Jungheung (, "Middle Prosperity":794, during the reign of King Seong.)
Jeongnyeok (, "Justice Era": 795 - 808 during the reign of King Gang.)
Yeongdeok (, "Eternal Virtue": 809 - 812 during the reign of King Jeong.)
Jujak (, "Sparrow Cinnabar": 813 - 817 during the reign of King Hui.)
Taesi (, "Great Beginning": 817 - 818 during the reign of King Gan.)
Geonheung (, "Founding of Prosperity": 818 - 820 during the reign of King Seon.) Hamhwa (, "United Peace": 830 - 858 during the reign of King Dae Ijin.) Note : King Dae Ijin, posthumous names are unknown, so usually they're called by their personal names.
Jeong-an Kingdom Wonheung (, "First Prosperity":976 - 986 during the reign of Oh Hyeon-myeong.)
Heung-Yo Kingdom Cheongyeong (, ("Heavenly Celebration"): 1029 - 1030 during the reign of Dae Yeon-Rim.)
Daewon Kingdom Yeunggi (, ("Prosperous Foundation") : 1116 during the reign of Go Yeong-Chang.)
Later Baekje Jeonggae (, ("Proper Opening"): 900 - 936 during the reign of Gyeon Hwon)
All these era names were used during the reign of King Gung-ye, who ruled Taebong from 901 to 918.
Mutae (, "Exalted Military" : 904 - 905 during the reign of Gung Ye)
Seongchaek (, "Sacred Book" : 905 - 910 during the reign of Gung Ye)
Sudeok Manse (?, ? "Ten Thousand Years of Flowing Power": 911 - 914 during the reign of Gung Ye) Jeonggae (, "Opening Rule" : 914 - 918 during the reign of Gung Ye) Note : In 918, General Wang Geon led a revolution, became the new emperor, and changed the country's name to Goryeo.
Cheonsu (, "Transmission of Heaven" : 918 - 933 during the reign of King Taejo.)
Gwangdeok (, "Brilliant Power" : 950 - 951 during the reign of King Gwangjong.) Junpung (, "Towering Plenty" : 960 - 963 during the reign of King Gwangjong.) Cheongae (, "Opening of Heaven" : 1135 - 1136 during the reign of Myo Cheong's Daewi state.)
Joseon Dynasty (1392 ~ 1897)
Joseon Dynasty of Korea integrated itself into the Chinese tributary sphere, and consequently used the era names of the Ming and Qing Dynasties of China for most of its existence.
Chinese era names are no longer used in modern Korean historiography.
Ming era names
Era name in Korean
1392 - 1398
Taejo, Jeongjong First era name in use during the Joseon Dynasty
1399 - 1402
1402 - 1424
Proclamation of virtue
1426 - 1435
Emperor Yingzong of Ming
Rectification of governance
1436 - 1449
1450 - 1457
Sejong, Munjong, Danjong, Sejo
Emperor Yingzong of Ming
Obedience to Heaven
1457 - 1464
1465 - 1487
Sejo, Yejong, Seongjong
1488 - 1505
Rectification of virtue
1506 - 1521
1522 - 1567
Jungjong, Injong, Myeongjong, Seonjo
1568 - 1572
Ten thousand calendars
1573 - 1620
1621 - 1627
Honorable and auspicious
1627 - 1637
Injo Korea was forced to officially use Qing era names after the second Manchu invasion of Korea in 1636 and 1637. The era name  , continued to be used informally after 1637 well into the nineteenth century, as the Manchu Qing Dynasty was often considered illegitimate by Korean scholars. Chongzhen 
Independent era names
Gaeguk (; ; "Nation's Opening"): used for the reign of Gojong of Joseon 1894-1895 Geonyang (; ; "Adopting Solar Calendar"): used for the reign of Gojong of Joseon 1896-1897
Gwangmu (; ; "Bright Valour"): used for the reign of Gojong of Korea, 1897-1907 Yunghui (; ; "Prosperous Brilliance"): used for the reign of Sunjong of Korea, 1907-1910
Republic of Korea
Daehan minguk (?, ? "Great Korean Republic" : 1948)
Dangun-giwon (?, ? "First Age of Lord Dangun" : 1948-1961) (?, ?, 1962-) Seoryeok-giwon
Democratic People's Republic of Korea Juche (, : 1912-)
Usage of Non-Korean Era names
Chinese era names were widely used, especially in the Joseon dynasty. During the Japanese occupation, Imperial Japan enforced its own era system.
North Korean government and associated organizations use a variation of the Gregorian calendar with a Juche year based on April 15, 1912 CE, the date of birth of Kim Il-sung, as year 1. There is no Juche year 0. The calendar was introduced in 1997. Months are unchanged from those in the standard Gregorian calendar. In many instances, the Juche year is given after the CE year, for example, 27 June 2007 Juche 96. But in North Korean publications, the Juche year is usually placed before the corresponding CE year, as in Juche 96 (2007).
"*Annals of the Joseon Dynasty,* third entry of February 28 1637". "?, ?, , , " : ""
Kim Haboush, JaHyun (2005), "Contesting Chinese Time, Nationalizing Temporal Space: Temporal Inscription in Late Chos?n Korea", in Lynn A. Struve (ed.), Time, Temporality, and Imperial Transition, Honolulu: University of Hawai'i Press, pp. 115-141, ISBN 0-8248-2827-5 .
http://www.ikgu.com/tt/717 A Guide to Korean Characters, 2nd Revised Edition, Bruce K. Grant, Hollym Publishing, Seoul, South Korea, 1982.
Sources of Korean Tradition, Volume One, Peter H. Lee, Yongho Choe, Hugh H.W. Kang (Eds), Columbia University Press, 1996 (Reign Name Translations, p. 21).