The official language of the Republic of Korea and the People's Republic of Korea; About 80 million native speakers living in various nations.
Romanization systems refer to a way of using Roman alphabet to transcribe languages of other writing systems. For Korean, which has the most logically designed alphabet of its own, romanization is not used much. First of all Koreans do not depend on romanization, because it is much easier to write in Hangul than Roman alphabet (partly because Hangul suits Korean and partly because Hangul system renders a syllable as one unit of writing, as in 한글 = Han-G(ue)l). But in the case of other languages such as Vietnamese, Chinese (as in Pinyin), and to certain extent Japanese (Romaji), a good romanization system was almost "required" because the langauges' own writing system did not reflect the correct pronunciation or did not encode any phonology at all (like Chinese characters). The fact that Korean speakers did not need Roman alphabet to scientifically represent their pronunciations made Romanization of Hangul particularly poor. Not many people care about romanization of Hangul, so it is no good.
Also, unlike Chinese or Japanese, Korean has large number of vowels (clearly shown by the number of vowels in Hangul ㅏㅑㅓㅕㅗㅛㅜㅠㅡㅣㅐㅔㅒㅖ ...). Although English and French too have large numbers of vowels, Roman alphabet has only 5 vowels (a, e, i, o, u) and 2 what I consider semivowels (y and h). (I believe this is why French and English spellings are so hard, but that's another topic). Because of the paucity of vowels in Roman alphabet, the numerous vowels in Korean can only turn to digraphs, like eu, ai, and so on. This solution did not turn out well because no English speaker can read romanized Hangul correctly (as in Hyundai, 현대, which should be pronounced more like hyun (like u in fun) de (like e in deism)).
With the relative indifference due to Hangul's efficiency and the small number of vowels in Roman alphabet, romanization of Hangul is very poor.
I have an idea to improve at least one bit of the terrible romanization of Hangul:
Korean vowel ㅡ is represented as "u" in romanization (as in 한글 'Han-gul'), but it is much better to represent it with no vowel. The reason is that as 'cl' in debacle (in Hangul 디바클), consecutive consonants with no vowels in English are pronounced with ㅡ. By romanizing 한글 as Han-gl, English speakers are better able to approximate and pronounce Hangul romanization better.