I started watching Asian dramas in early 2015, and the first drama I've ever watched was Boys Over Flowers (2009). I was immediately sucked into the K-drama world, and I started off with the classic ones and gradually developed my taste to include many other drama genres. This list includes all the dramas I have finished as well as some that I didn't finish but got more than half way through. I am planning writing reviews for some of the dramas on this list, and feel free to request drama reviews through the chat box on this site.
This list is not in any particular order (ranking, chronological, etc.), but I have divided it up into language (Chinese, Korean, Japanese) as well as sub-categories of different genres. Romance is a tricky category because most Asian dramas have a romance component to them, so the ones in the romance category are the ones that don't really have a larger plot (eg. corruption) or distinguishable setting (eg. historical) apart from it being a romance drama. Also, just because I have watched it, doesn't mean I necessarily recommend it, and I can make a separate list of those I recommend and those I don't. For now, enjoy!
CHINESE DRAMAS
Historical
The Untamed
Ten Miles of Peach Blossoms
Ashes of Love
Gaming
The King's Avatar
Love O2O
Romance
A Love So Beautiful
My Amazing Boyfriend
My Mr. Mermaid
Find Yourself
Unrequited Love
Meteor Garden
Accidentally in Love
When I See You Again
KOREAN DRAMAS
Crime/Corruption
Signal
Healer
Stranger
Remember: War of the Son
Tunnel
Voice
Criminal Minds
K2
While You Were Sleeping
Solomon’s Perjury
City Hunter
Historical
Moon Lovers Scarlet Heart
Hwarang
Scholar Who Walks the Night
Ruler: Master of the Mask
Rookie Historian
Classics
Boys Over Flowers
Secret Garden
You’re Beautiful
Heartstrings
Dream High
Supernatural
My Love from Another Star
Goblin
Bride of the Century
Legend of the Blue Sea
Memories of Alhambra
W
Hey Ghost Let’s Fight
Abyss
School Setting
Extracurricular
School 2015
School 2017
Heirs
Weightlifting Fairy
Sassy Go Go
To the Beautiful You
Moorim School
Page Turner
Cheese in the Trap
Coming-of-age/Finding Yourself
Itaewon Class
Hospital Playlist
It's Okay to Not be Okay
Andante
Romance
Crash Landing on You
Weightlifting Fairy
Flower boy next door
Doctors
Pinnochio
Uncontrollably Fond
Love Alarm
Her Private Life
My Suspicious Partner
Romance is a Bonus Book
She Was Pretty
Cinderella with the Four Knights
Birth of a Beauty
Marriage, Not Dating
Introverted Boss
My Secret Romance
Sweet Stranger and Me
My Only Love Song
JAPANESE DRAMAS
Good Morning Call
Switched