Hana Yori Dango!! 
Mine was either the Gokusen series or the original Hana Kimi :)
1 Litre of tears, it also was the one who started my love for asian dramas and movies
Virgin Road (Sorimachi Takashi). Loved every minute of it!
Hana Yori Dango :D After I watched two japanese movie, I needed to see something similar and then I got hooked with asian dramas.
Either Kurosagi or My Boss My Hero, can't remember which, love them both still :)
The first one I completed, I think, was Mr. Brain. I was watching Ando Natsu at the same time, and never totally finished it.
I've only watched 1 so far: Tatta Titotsu no Koi
Hana Kimi I think, watched it back in 2008
Boku no ita Jikan...I watched it really quickly, too. Like 3 days? I was so hooked.