Ughh That's a hard list to make but I'll try.
Secret Poison and Love is Move
Super Junior No Other
Shinee Replay and Ring Ding Dong
Chocolat One More Day
5Dolls Like This Like That
Sunny Hill Grasshopper Song
MBLAQ Smoky Girl and Cry
Infinite [BTD (Before the Dawn], (https://youtu.be/3UggIMs8pdE) Destiny and Be Mine
Rania [Dr. Feel Good]
4Minute Huh and Mirror Mirror
Hyuna Change
Hello Venus Do You Want Some Tea?
Rainbow Blaxx Cha Cha
Big Bang [La La La] and [https://youtu.be/rc-cHSzK5-U] We Belong Together
Gummy There Is No Love
Tablo No Tomrrow
G.Na I'll Get Lost You Go Your Way
Miss A Breathe and Goodbye Baby
Beast Beautiful Night
Ukiss Standing Still and Neverland
BAP Warrior
Okay that's all I'll probably post cause I want to let others make their list. I tried to list songs before 2012 but a few made it in the cracks. Nonetheless, these are some (and I say this lightly) of my favorite older kpop songs.