The state of Korean Romanization is a total disaster. After I learned Hahn.geul (the Korean script) I got rid of all of my textbooks that used Romanization because they were more confusing than they were helpful. Still, Korean needs a better Romanization system for foreigners visiting the country. There is a way to Romanize which is much closer to the way that words are actually pronounced in Korean.
Every book you pick up that has Romanized Korean in it seems to use a different system and they are all terrible. This is because in many cases there is no direct mapping between some Korean sounds and English sounds. Another reason is that there are many languages that use the Latin alphabet and they don't all pronounce every letter or diphthong in the same way. In 2000 the Korean government came up with yet another system (Revised Romanization) which, in my opinion, didn't do enough to fix the problems in the existing systems.
Here's one example for the Romanization of wall (벽):
As you can see, in some systems the initial "ㅂ" is transliterated as a "b" and in some it is a "p". I'm not entirely sure that this is something that can be addressed in a Romanization system because the sound in Korean is between the "p" and "b" in English. One of the biggest problems with the older systems is the use of accents to denote different vowels. Surely there must be a way to write out the vowels so they can be read without having to look up how the accent transforms the vowel. That is one good thing about the new system: no accents.
I believe the "eo" comes from the French who gave us "Seoul". This always trips up my non-Korean-speaking friends. In my system I have taken the sound of the Korean vowels and changed them so that the sound of the vowel is unambiguous. In this case "eo" is more like "uh" and then "oo" smashed together. In my system "서울" is "Suh.ool". Periods are placed between consonants.
My wife attended "Soongsil" University. I believe it was Romanized this way because it is transliterated. If you take each component of "숭실" and turn it into a list you would get "ㅅㅜㅇㅅㅣㄹ". Transliterate that without context and you would end up with something similar to "Soongsil". However, in Korean if you have a "ㅅ" followed by certain vowels it actually becomes "sh". Another confusing bit of the existing transliteration is "ㅣ" to "i". Usually without an "e" the "i" is short like in "sit". The actual sound is usually more like "ee" in "eel". When you meet a Korean whose last name is Lee their actual name is actually just "ee". There is no "l" sound at all in the beginning of their name (unless they are North Korean... but you probably won't have too many chances to meet many North Koreans). In the system I have created "숭실" becomes "Soong.sheel" because that's how it's actually pronounced.
The system I have come up with is not a direct transliteration. It first runs the Korean string through pronunciation rules and then it is transliterated from the output of the pronunciation engine.
You can try it out below or on dongsa.net but I doubt that it will work in older browsers or Internet Explorer: