So I recently got into JDramas and know almost nothing about some of the best dramas and actors from Japan. Anyone have suggestions? I usually like watching things in the romance/manga/war/medical genre.

I've seen:

Taiyou No Uta

Ouran High School Host Club

Mirai Nikki

Liar Game/Liar Game 2

Kazoku Game

Death Note

Attack No.1

1 Litre of Tears

I plan on watching:

Byakyuko

Code Blue/Code Blue 2

I mostly watch J-Dramas you can try: 

Hanzawa Naoki - business themed drama

The Great White Tower- medical themed drama and overall one of the best dramas I've seen.

These are my favourite:

Bitter Blood
Kazoku Game
Jin season 1 and 2
wohaaa sooo many *_* 
Nodame Cantabile, Nobuta wo Produce, My Boss My Hero, and Hana Kimi - are classic manga adaptations
Switch Girl, and Yamada and the Seven Witches - also shojo manga adaptations
Buzzer Beat
Pride
Long Vacation
Date
Dear Sister
The Memorandum of Kyoko Okitegami
Orange Days
Rich Man Poor Woman

I'm not familiar with medical or war dramas
you cant quote people anymore on these forums but anyway

winnie - 1033 Posts
I mostly watch J-Dramas you can try:  Hanzawa Naoki - business themed drama The Great White Tower- medical themed drama and overall one of the best dramas I've seen. 8 hours agoNadia - 6 Posts These are my favourite: Bitter Blood Kazoku Game Jin season 1 and 2 6 hours agolovelySawako - 1 Post wohaaa sooo many *_*  3 hours agoSimplifica - 7 Posts http://mydramalist.com/list/q1XzglP3 for you :) 21 minutes agosylwia - 76 Posts Nodame Cantabile, Nobuta wo Produce, My Boss My Hero, and Hana Kimi - are classic manga adaptations Switch Girl, and Yamada and the Seven Witches - also shojo manga adaptations Buzzer Beat Pride Long Vacation Date  Dear Sister The Memorandum of Kyoko Okitegami Orange Days Rich Man Poor Woman I'm not familiar with medical or war dramas

I agree with the above. 
Buzzer beat, Hana Yori Dango (i loved the entire j-drama series 1-3 plus the movie) , Crying out love in the center of the world (same mains as Bykuyaku) , LIFE, Proposal Daisakusen- are all among my top favorites!!
I recommend
-From Five to nine 
-Hana Yori Dango
-Rich man, Poor woman
-Koizora (drama)
Dear Sister
Hana Kimi
Last Friends
Ghost Friends
Sunao Ni Narenakute
Hana Yori Dango 
Itazura Na kiss Love in Tokyo 
I know that you have watched some of these:

Maou
1 Litre of Tears
Summer Snow
Soredemo, Ikite Yuku
Boku No Ita Jikan
BORDER
Orange Days
Nazo No Tenkousei
Love Shuffle
Legal High
Kazoku Game
Jin
Hanzawa Naoki

These are all the jdramas that I've given a 10/10
http://mydramalist.com/list/P4YWxqqL
Gochisousan
The Emperor's cook
Samurai Highschool
Date
Hanasaki Mai ga Damattenai

Flowers for Algernon, honestly killed me waiting for the subs for the final 3 episodes but they're up now :)