Here's another list. I tried to mention songs that are not that famous (and I was like what the ...? way?). Again. This list is really random, so no top 10, not just K-pop (other genres too). Here we go:

korean music and xxinnara image
xxinnara - paralysis
kmusic, korean music, and korean hip hop image
Jin Doggae feat. J.Fla - Tic Toc
hip hop and baechigi image
BAECHIGI - SHUT UP (feat.솔지 of EXID)
korean music, kindie, and y.sookyoung image
Y.Sookyoung - Surge
kpop and elizabeth kpop duo image
Attention! Really wierd music video -> Elizabeth - Ppappa Pierrot
kmusic and klang korean singer image
Klang - The wanted
kmusic, korean music, and rude paper image
Rude Paper - One Blood (check other songs too!)
korean music, 24hours, and kindie image
24HOURS - Our Night
korean music, kindie, and sugar donut image
Sugar Donut: Beautiful Life & Imagine, Close Your Eyes
korean music image
ByeByeSea: My Mind Talks & Devil
kpop, unicorn, and 유니콘 image
Unicorn (all their song from their 2nd mini album): Blink Blink, Sun Shower and I Need You Tonight
c-luv, taewan, and kimtaewan image
Taewan - Problem
Okay. Guckkasten is one of my fav K-rock bands and I really love their songs (Montage, Manicure, 변신, Pulse ecc.). If you like that kind of style please check thier albums.
korean music and clazziquai project image
CLAZZIQUAI PROJECT - #궁금해 (#Curious)
kpop and d.holic image
After "Chewy" D.holic made a comeback with "color me rad", which I really like it. Sadly they disbanded :/
ukiss, neverland, and AJ image
U-Kiss has many great b-side songs. My fav are: Heartless, Someday, Te Amo, Amazing, Top that
kpop, subin, and dalshabet image
Subin (of Dalshabet) - Circle's Dream
korean music, kindie, and fantastic drugstore image
Fantastic Drugstore - Before Sunrise
korean music, kindie, and the solutions image
THE SOLUTIONS - Ticket to the Moon
korean music, kindie, and stellarjet image
Stellarjet - I don't like you
f(x), amber, and luna image
F(x) - Beautiful Stranger

I will stop here and maybe make a part 2 (or even part 3 ecc.) in nearly future.