peekyou.com is one good example. It is a website which works by searching a person's name against information held on social network sites like Facebook, Google + and MySpace.
Using social networks to find people in Korea
The widespread use of such networks means that pretty much everyone who owns a computer (or even just a mobile phone) is contactable through a profile they've created on one of the many social networks.
If you're trying to get in touch with someone in South Korea there's a good chance you'll be able to get hold of them via the internet. South Korea is one of the most technologically-advanced countries in the world (4G and WiFi are even available on the subways!!!) so rest assured that it's very likely the person you are trying to find will be part of at least one social network.
The Korean Facebook?
Whilst this might be a very effective way of tracing a friend in Korea, be warned that parts of the site are in Korean and you may need the help of a Korean-speaker to navigate certain pages.
Luckily SK Communications have developed an English version of CyWorld, with the 'Find People' page being one good suggestions for your search.