I starting to shift into jdramas actually this month after I watch the 1 little of tears. So I hope You can recommend me some dramas for me to watch. Just state your top 5 jdramas.. tnx a lot!
Since I just started to watch it my top 5 are:
1. 1 little of tears
2. Nobunaga Concerto
3. Nobunaga Concerto Movie
4. Rich Man Poor Woman--**I forgot to add this one :)
5. Rich Man Poor Woman Movie
In watch list Please love the useless me, Hapi Mari, From Five to nine 
Separated by Genre....  -----> First 5 are CLASSICS !! .... and Must-See for beginners! 

Classics ... mainly Manga Shoujo :
Hana Yori Dango ---  
Hanazakari no Kimitachi e  ---  Hilarious Romp
Nobuta wo Produce ---
Gokusen --- 
Nodame Cantabile --- 

More Classics:
Buzzer Beat --- 
GTO --- 
My Boss, My Hero --- 
Orange Days --- 

Popular Rom-com:
Last Cinderella --- 
Love Shuffle --- 
Long Vacation --- I didn't like it much, weak characters, but others loved this

Romance:
Tatta Hitotsu no Koi ---
Pride ---
Kamisama Mou Sukoshi Dake --- 
Kou Kou Kyoushi (1993) --- 

Classic Drama .... Dark and/or Slice-of-Life and/or Other ...Etc...:
Soredemo, Ikite Yuku ---  
Liar Game --- 
Piece --- 
Mother --- 
Ice World --- 

More Classic Drama:
Maou --- 
Long Love Letter ---  
Ikebukuro West Gate Park --- 
One Million Stars Falling from the Sky --- 

Taiga (historical):
Tenchijin --- 
Gunshi Kanbei --- 

Depends on the genre that you like! :)

Romance Dramas:

http://mydramalist.com/1344-asuko-march (also school/frinedship)
http://mydramalist.com/49-buzzer-beat (also sports)
http://mydramalist.com/782-beautiful-life (also drama/tragedy)
http://mydramalist.com/69-koishite-akuma (also school/vampire)
http://mydramalist.com/2905-kingyo-club (also school/drama)
http://mydramalist.com/412-good-luck

Romantic Comedy Dramas:
http://mydramalist.com/2985-hanazakari-no-kimitach... (also school/friendship)
http://mydramalist.com/2277-ikemen-desu-ne (also music)

Comedy Dramas:
http://mydramalist.com/22-atashinchi-no-danshi (also family)
http://mydramalist.com/82-attention-please
http://mydramalist.com/2988-nobuta-wo-produce (also school/friendship)
http://mydramalist.com/102-ryusei-no-kizuna (also family/mystery)
http://mydramalist.com/151-dragon-zakura (also school/drama)

Crime/Suspense Dramas:
http://mydramalist.com/7116-limit (also action/school/psychological/drama/life)
http://mydramalist.com/248-shinzanmono (also detective)
http://mydramalist.com/15229-siren (also detective/romance/thriller)

I loved all the dramas I've mentioned above!! :)   Hope you like them too!!
1 litre of tears
koizora
Hana kimi
gokusen
Switch girl
All time favorite, must watch: Hana Yori Dango


ROMANCE

Buzzer Beat
Love Shuffle
Pride
Tatta Hitotsu no koi
Hotaru no Hikari


DRAMA

Byakuyako
Koizora
Taiyou no kisetsu
Soredemo, ikite yuku
Sekai no Chuushin de, Ai wo sakebu

COMEDY

Atashinchi no Danshi
Hanazakari no Kimitachi e
Ouran High school host club
Mei-chan no shitsuji
My Boss, my hero


SLICE OF LIFE

Nodame Cantabile
Rookies
My girl
GTO
Gokusen
Dragon Zakura


SUSPENSE (here I'm going to exceed form 5, because japanese suspense dramas are very good, do try them, this dramas are 10, 9 and 9.5 for me)

Maou
The quiz show 2
N no tame ni
Ryusei no Kizuna
Liar Game
Kazoku game
Kurosagi


SPORTS

H2



MOVIES

Death Note
Rurouni Kenshin
Bokura ga ita
Heroine Disqualified
Paradise Kiss


Hope this helps you :D
I second the lists above :) 
wow!thanks a LOT!!! :) starting to download all of this!! :) thanks! :)
Hope you like them all! :)
I'd also recommend Okitegami Kyoko no Biboroku! It seems pretty underrated from what I gather through people's recs, but it was one of the first jdramas I watched and really enjoyed, so I'd say it's worth a shot :)
Not going to repeat the dramas that other people mentioned but I would like to add some:

Date - Koi to wa Donna Mono Kashira - if you're in a mood for a different kind of rom-com (I know it doesn't seem that way from the premise but trust me).
LIFE - a pretty heavy drama dealing with bullying. "What doesn't kill you, makes you stronger" pretty much sums up the story. 
Minami-kun no koibito: My little lover - in my opinion a really well done cliche rom-com. 
Liar Game
Hana Kimi
Atashinchi no Danshi
Ouran high school host club
Legal High
Beautiful Life
Hotaru no Hikari 
Hapi Mari
From 5 to 9
Pride
great recs thanks all
(you should watch boku no yabai tsuma too)
Nobuta wo Produce
Hapimari: Happy Marriage?!
Nigeru wa Haji da ga Yaku ni Tatsu
Tatta Hitotsu no Koi
Love Generation