Ik it sounds kind of odd, but you know Gangnam Style got popular yet all these other grousp are kinda being ditched when they have a lot of skill.

I guess for a first I'll give you the names of some male kpop groups and solo artists:
Bigbang
Infinite
SHINee
EXO
CNBLUE
FTISLAND
Teentop
TVXQ
JYJ
JYP
Jay Park
U-KISS
B.A.P
B1A4
B2ST/BEAST
ChAOS
SS501
Super Junior
2PM
2AM
Z:EA

And some girl groups:
f(x)
2NE1
After School
Sistar
Girls' Generation/SNSD
4MINUTE
G.NA
IU
T-ARA
Kara

Do you like upbeat songs? Then I'd suggest these songs:
Bigbang - Fantastic Baby
Infinite - The Chaser
B2ST - Beautiful Night
JJ Project - Bounce
Bigbang - Feeling
B.A.P - Crash
CNBLUE - Love Girl
Block B - Nanlina
T-ARA - Yayaya
2NE1 - I Am The Best
f(x) - Hot Summer
SHINee - Sherlock
Super Junior - Mr Simple
U-KISS - Neverland
EXO - Mama
Tasty - You Know Me

Or maybe you like Ballads?
JYJ - In Heaven
Infinite - Only Tears
2PM - Heartbeat
FTISLAND - Girls Don't Know
CNBLUE - Teardrops in the rain
Xia Junsu - Uncommitted
Bigbang - Haru Haru

Or maybe upbeat ballads?
B1A4 - Baby I'm Sorry
2NE1 - Ugly
EXO - What Is Love
FTISLAND - Severely

Or fierce upbeat songs?
B.A.P - Unbreakable
B.A.P - Warrior
EXO - Machine
EXO - History
B.A.P - No Mercy

Or solo songs?
Daesung - Wings
T.O.P - Turn It Up
G-Dragon - One Of A Kind
G-Dragon - That XX
Psy - Gangnam Style
Jay Park - Know Your Name
Dara - Kiss
Seungri - What Can I Do
Seungri - VVIP
Xia Junsu - Tarantallegra

Or love songs?
Bigbang - Bad Boy
Bigbang - Love Dust
Teentop - Be Ma Girl
Teentop - To You
2NE1 - I Love You
B1A4 - Beautiful Target
CNBLUE - Love
f(x) - Love
Infinite - I Like You

And generally just kickass songs:
CNBLUE - I'm a Loner
EXO - Two Moons
GD&TOP - High High
Taeyang - I'll Be There
HyunA - Bubble Pop
Infinite - Be Mine
NU'EST - Face
JJ Project - Before The Song Ends
SHINee - Lucifer
Super Junior - Spy
Super Junior - Sexy, Free and Single
T-ARA - Bo Peep Bo Peep
Miss A - Bad Girl Good Girl
SS501 - Love Like This
2NE1 - Can't Nobody
Kara - Step
2pm - Hands Up
U-KISS - Te Amo
Wonder Girls - Like This
MBLAQ - It's War

However odd it sounds to listen to something in a different language it's definitely worth a shot ^^
Hope this helped ;D (/*-*)/