doesn't have to be all the episodes but something with a good pace.

Thanks...

Definitely Missing Noir M
I hear your voice

mostly jdramas - 
Doctor X
Hero
Code Blue
Gokusen
Trick(Japanese)
God's Quiz (Korean)
Subete ga F ni Naru(Japanese)

Trick and God's Quiz are a bit more episodic, with multiple seasons. Subete ga F ni Naru kind of fits, but there is only one season and a definate overarching theme.
+1 God's Quiz
+1 Missing Noir M


Gloomy Salad Days
Seonam Girls
The Quiz Show
Special Affairs Team TEN
Mysterious Summer is the best episodic show ever! :P highly reccomend, each story is mind blowing. You can watch each episode in any order, and show any of them to people who haven't seen earlier episodes. (I showed my mom about 2-3 of my favorite episodes out of order^^)
The Quiz Show
The Quiz Show 2
Mahoro Ekimae Bangaichi

Liar Game (Korean) isn't quite episodic but contains different "games" every two episodes with an underlying story. There are also dramas like Signal and I Remember You that contain different cases throughout the series with an underlying story that are the perfect mix between a continuous drama and an episodic one.
Beginners!
BORDER
Opas: The Series Season 1
Otomen
ST ~ Aka to Shiro no Sousa File
Mysterious Incredible Terminator
Psychometrer Eiji

Dr. Frost.
Missing Noir M
Borders
God's Quiz
Special Affairs Team TEN 1 & 2
The Quiz Show
Love me if you dare
The Devil
Control - Hanzai Shinri Sousa
It's Okay That's Love
Evil Minds
Madame Antoine
I remember you (?, not very sure but If I remember it correctly, yes)


These are all what I remember, I also included dramas which are not very episodic. :)
Sweden Laundry for something different - She can tell the future by touching someones clothing. I thought it was quite good but i like supernatural
I Remember You (kdrama) would indeed qualify I guess @ScarletStar
Just like the Vampire Prosecutor/Detective (k)dramas, it has generally a new investigation every episode, but there's an overarching storyline behind it too, which becomes quite important in I Remember You. 

Two others that should qualify:
The Master's Sun (kdrama)
Gokusen series (jdrama)