Hmm, I have watched a decent amount (by my standards) of Jdrama's, and there are some, I have loved, but would never recommend to a Jdrama newbie, most of the suggestions in this thread are of that sort.. And then there are the ones regardless, I would recommend because they are awesome...In that category the already recommended ones would be:
Bloody Monday
Last Friends
Love Shuffle
Now the ones that I really really enjoyed that I haven't seen mentioned, that doesn't mean they weren't just means I wasn't paying close attention..
Hotaru no Hikari both seasons- About as Rom/Com as Jdrama's get imo..
LADY~Saigo no Hanzai Profile~
MR. BRAIN
Sunao ni Narenakute
Uta no Onii-san
Koshonin