If you like R&B and even if you don't i would most certainly give T (Tasha) a try she is one of the most underrated artists in Korea
http://www.youtube.com/watch?v=gY1PTDpysR4
Lee Soo Young also is a good artist though she doesn't release as much anymore; she used to do a lot of ballads
http://www.youtube.com/watch?v=glef1XK4rak
Brown eye girls are popular now due to their latest work but their older material was just as good if not better
http://www.youtube.com/watch?v=MAwOyArpfRE
Shinhwa, once again are popular but older then the teeny boppers. I still find that i can go back to their material and not be let down.
http://www.youtube.com/watch?v=FvgYHciiUmo
Classiquai- completely underrated even if they are somewhat known.
the only group i know that can execute a calm feeling to a techno song.
http://www.youtube.com/watch?v=KOW0fihERE0
W& Whale are a bit underground but the female singers voice is really powerful
http://www.youtube.com/watch?v=QhovBL7D4bY
and finally (i'm surprised that no one mentioned her ) but J is a phenomenal artist (once again waning popularity (most likely because she's Korean-American
http://www.youtube.com/watch?v=HqYyveq0dVA
Hope that helps