I LOVE Japanese dramas, they're short and sweet. I recommend:
*-Attention Please! (The first jdrama I've ever seen... The one that began it all for me.)
*-Hanazakari no Kimitachi e
*-No buta Wo Produce
-Gokusen 1 & Gokusen 2
-Orange Days
-First Kiss (Inoue Mao from Hana Yori Dango!)
-Liar Game
-Jotei
-Kurosagi
-Tokyo Wankei
-1 litre of tears (So sad, but very very inspiring. It'll make you want to live life to the fullest)
-Ace wo nerae
-Proposal Daisakusen
-Tatta Hitotsu no Koi
-hotaru no hikari
-One Million Stars Falling From the Sky (Sora Kara Furu Ichioku no Hoshi)
*= extremely recommended. But these are all great dramas!
Here are some sites you can use to watch them:
aznv http://aznv.tv/en/ (The best one in my opinion. You can stream full episodes without breaks here, but it requires registration. Don't worry though, it's free and painless. This is the main site I use for watching dramas.)
Mysoju http://www.mysoju.com/
Crunchyroll http://www.crunchyroll.com/
---TIP: Usually I use aznv to watch dramas but if they have it, I go to mysoju, and if even Mysoju doesn't have it, on to crunchyroll. i usually don't have to go beyond these 3 sites, but you can also watch on these sites:
http://www.veoh.com/
http://chinkymovies.blogspot.com/ (For downloading dramas)
Youtube http://www.youtube.com/