Until now I've been watching kdramas almost exclusively. I want to branch out to jdrama now. I love romance, fluff, melodramas. Police shows are okay too as long as they aren't too dark and gritty. I also like shoujo manga/anime adaptations. See my list to get a better idea. What would you guys recommend?

Nodame Cantabile

Long Vacation

Love Shuffle

Saigo Kara Nibanme no Koi

Neko Zamurai (if you like cats)

Love Revolution

I also second the recommendation for Bitter Blood and Kekkon Dekinai Otoko.

 kitty10:
I also second the recommendation for Bitter Blood and Kekkon Dekinai Otoko.

Kekkon Dekinai Otoko is creme de la creme :)

Thirding Kekkon Dekinai Otoko! It's a great and fun drama. Also seconding Suki na Hito ga Iru Koto, it's a cute summery romance

Adding:

Ashi Girl - a fun manga adaptation of a time travel historical series! 

Thanks to everyone! I will definitely check them,

Definitely watch Buzzer Beat

Also the classic:  Nobuta Wo Produce

Ossan's Love is pretty great.

Not entirely fitting your description, but I recommend this drama to anyone who want to watch a  Japanese series, as it is my favourite. It is called Kazoku Game.