@ViolinGal
First of all your list is veeeery long :O
But here is what I recommend:
Pride
Hana Yori Dango (both seasons, plus watch the movie)
Love Shuffle
Secret Garden
Bokura ga Ita (both movies)
Buzzer Beat
Heroine Disqualified
I'm Sorry, I Love You
Kazoku Game
Itazura na Kiss (both seasons)
Delightful Girl, Choon Hyang
Goong
GTO
Kimi ni Todoke
Koizora (you only need to watch one, the story is pretty much the same so I recommend the drama over the movie)
Kurosagi
LIAR GAME (both seasons, plus add the movie)
Mask
Nodame Cantabile (the drama, the 2 specials and 2 movies)
Rurouni Kenshin (3 movies)
Ryusei no Kizuna
Tada, Kimi Wo Aishiteru
The Moon that Embraces the Sun
Zenkai Girl
Cain and Abel
Full House
One More Happy Ending
Sunao ni Narenakute
Bara no nai Hanaya
Can You Hear My Heart
Hotaru no Hikari
My Boss, My Hero
Nobuta Wo Produce
Proposal Daisakusen
ROOKIES
Summer's Desire
Cunning Single Lady
Easy Fortune Happy Life
Falling for Innocence
Gokusen (this has 3 seasons both are independent one form the other so if you like season 1 you can watch the other 2 seasons, If not leave it like that)
MARS - Tada, Kimi wo Aishiteru
Orthros no Inu
Tokyo DOGS
Akai Ito
Hana Kimi
Heartstrings
Mary Stayed Out All Night
My Lucky Star
Soredemo, Ikite Yuku
Ao Haru Ride (if you like manga I recommend you read the manga is way better than the movie, the movie was not so well adapted)
Flower Boy Next Door
Que Sera, Sera
That Fool
The Girl Who Sees Scents
Bloody Monday (if you like season 1 whatch season 2 also)
Boku no Ita Jikan
Death Note (you have the drama on your watch list, but I recommend to watch the movies they are better)
Ikemen Desu Ne
Shut Up: Flower Boy Band
Zettai Kareshi
Ouroboros
I also notice you have several old dramas on your list, I would recommend to try to watch them before watching something airing or recently. Because I've found that sometimes when they are too old even though the story is really good the old fashion, style, hair, etc, won't let you concentrate in the story until like 4 episodes latter. But that's my opinion.
Well hope this helps you.