A search on Distrowatch for Korean linux distros returns 7 results, 5 of which have been discontinued. Of the two that are still active, one is AnNyung Linux, a localized Korean distro based on RedHat/CentOS 6 while the other is Asianux. Ticketmonster Korea (which was acquired by Living Social of the US one year ago) runs AnNyung Linux exclusively on its servers.
I remember back in 2005, the Korean word-processing software company Hancom came out with 'Asianux,' a Korean-localized version of RedHat, but that never really went anywhere. It was an outgrowth of previously discontinued efforts represented by Haansoft Linux (2004) and Hancom Linux (2002). Hancom doesn't really get open-source (it tried to charge business end-users of the 2 distros above), and even the .hwp binary file format for its word-processing files was closed until 2010 (but still many file streams in .hwp remain undocumented. There is a github project called pyhwp that is also available through pip, that is trying to reverse-engineer the .hwp format, however). I tried to download the latest v4 release of Asianux, but the page 404's after the images to download have been selected.
IMHO, Korea should follow the lead of Japanese and Chinese-community re-spins of popular and user-friendly distros like Ubuntu and Debian. Prime examples are the popular Deepin Linux (based on Ubuntu) created by Chinese users and Vine Linux (based on Debian Testing) created by Japanese users, both of which are active projects with recent releases in July and September 2012. Maybe I should use Remastersys to create my own localized Korean re-spin of either Ubuntu or Debian...it would be the first non-RedHat Korean localized linux in history!