Romance: Last Cinderella, Hotaru no Hikari, Rich Man Poor Woman, Hana Yori Dango and, if you're in the mood to cry your eyeballs out, 1 litre of tears.
Detective: Kagi no Kakatta Heya, BORDER (just came out last season and I really enjoyed it :3 ), Kurokouchi (I really liked it, it was a different approach to a detective drama, it was very interesting), Hard Nut! (this one was maybe a little bit sillier, but I just loved it way more than I expected to :D ), Ataru.
There's also, Boss, Galileo, Dr Brain which are very popular amongst J detective dramas but aren't some of my personal faves.