Nobuta wo Produce
dinner
Biblia Koshodou no Jiken Techou
Love Shuffle
Bloody Monday (seasons 1 & 2)
Subete ga F ni Naru
I have seen only a dozen or two Jdrama but most of them turned out so good so I would recommend that you should try anything that comes to your mind or your sight (that doesn't mean every Jdrama is good, its only that (what people consider bad can be so good and the vice-versa , its a matter of taste )

Anyway I have prepared this list of some of the best JDrama (based on opinions from this community) , you may use it for reference or anytime you wanted to find a good Jdrama

Japanese Drama Masterpieces
recently watched 

Rookies >> the best nothing more need to be said :P

Water's boy >>> all three seasons of it are awesome :) 

RunAway~Aisuru kimi no tame ni >> really good it's new .. talk about runaway prisoners who each have goal for breaking out and try to reach it while on run .




i am not into war & medical genre and dont like heavy dramas much. so here are some dramas from manga adaptations;

GTO- shounen- ex-delinquent becomes school teacher

Gakusenshoujo- mafia heiress becomes school teacher, school fight

Hana kimishoujo- gender bender- romcom- original version of to the beautiful you

Hana yori dango- shoujo- original version of boys over flowers

Hataraki man- seinen- romcom- business

Holyland- seinen- psychological- street fighter

Hotaru no hikari- josei- older version of switch girl characters

Ikemen desu ne- gender bender- remake of you're beautiful, not manga

Kimi wa petto- josei- career woman gets a cute boy as her pet

Koizora- shoujo- heavy drama, school

Mei-chan no shitsuji- shoujo- girl gets a butler at a special boarding school

Nobunaga concerto- seinen- time travel- follows real history

Drop- shounen- bromance- delinquents

Rich man poor woman- romcom- business, not manga

Saba doru- romcom- aged woman acts as a teen idol, later manga

Switch girl!!- shoujo- girl wearing a perfect character mask outside, at home she is extremely opposite.

Yamato nadeshiko shichi henge- shoujo- weird scary girl moves in with 4 eye candy boys

Yankee-kun to megane-chan- shounen- school, female ex-delinquent meets her male version

Zettai kareshi- shoujo- career woman gets a robot as boyfriend

High school debut- shoujo- baseball maniac muscle girl tries to change herself into a fashionable cute girl to get a bf




also some movies from mangas;

Crows Zero- shounen- delinquents, school fight

Kaiji- seinen- gambling

Space Brothers- seinen- unemployed engineer man following his dream of being an astronaut

Rurouni Kenshin- seinen- sword fight

Heroine disqualified- shoujo- romcom, school

Dance Subaru- shoujo- girl following her dream of being a ballet dancer



i did not include the ones i dropped & on my ptw (except for kenshin, it seems as a must) and tried to recommend the ones not on any of your lists.










BORDER
Freeter, Ie o Kau.
From five to nine
Hana Kimi (2007)
Ouroboros
Maou
Stand Up!!