Hi mate? You allright? What's up? None of these will quite do the trick in Korea...
Recently, walking in the hallway of the Elementary school where I teach, I saw an interesting sign on the wall outside the kids' bathrooms. It said "Meonjeo Insa Hamnida", meaning "Be the first to greet". It's a reminder for the kids with their short attention spans and energetic minds to always be respectful, mind their manners, and greet the teachers (or anyone older than themselves), first.
Often kids would come running into the staff room on a quick errand and, in their haste to accomplish a given task, would run to a cupboard or person without giving greeting a second thought. "Insa!" (Greet!) would come the stern rebuke from an educator.
Like in any culture, Koreans regard a greeting as a very important part of showing respect. The Korean language not only has a couple of different phrases from greeting, with honorifics increasing with the age of the person you are greeting, but also a few interesting set phrases after the initial "Hello". Sort of like we use "Nice to meet you" or "How do you do?" in English. The Korean versions though, are more formal and respectful.
If you're not interested in grappling with and obtaining some sort of fluency in this Asian language, you should at the very least consider memorizing the Korean greetings and one or two phrases for when you meet someone for the first time. When you greet Koreans in their own language (apart from the obvious fact that many of them will not understand you if you start babbling in English), there's an immediate openness and helpfulness in their demeanor.
You will of course, also impress everyone from your employer to your students when they realize, that despite what they've been believing for years, other people can also speak Korean! Even if it's just a greeting...
Here's a list of the basic greetings and introductory phrases in Korean:
Ann-yeong-haseyo? : Hello
The first Korean word any foreigner should learn. Literally meaning "How do you do?" it should be spoken with a rising intonation towards the end, to indicate a question. This is the standard greeting everyone uses and is formal enough to be used for older people as well.
Ann-yeong-hashimnika : Hello
Same as Annyeonghaseyo but more formal. This is should be used with your boss and people much older than you. Since you're a foreigner no one would ever be offended if you used the first greeting with them, but by bothering to learn a more formal one, people will see that you care.
Pangapsimnida : Nice to meet you
Same as in English, use it right after Annyeonghaseyo.
Tjal Butakdirimnida : I hope we get along well
Literally meaning "I shall be in your debt", this is also a very formal phrase normally used between employers or business people. Pop this one to your principal the first time you meet and his eyes will fall out!
Songhami Otteoke Dweyseyo? : What is your name?
Formal way of inquire someone's name. Commonly used between people who meet for the first time.
For a more comprehesive list of Korean phrases, including a free downloadable phrase book, see this article.