Yes Tokyo Dogs is a cop show but it's more comedic, bloody monday is a bit more crime thriller type
Another awesome cop drama than i absolutely loved was Boss. that was epic all around.
if you want something like a family comedy/drama i liked Brother Beat and At home dad a lot too, those are older shows though.
my first jdrama was hana yori dango, there's 2 seasons and a movie i watched it cause i loved the anime and thats how i got interested in jdramas
some of my favourites were orange days, honey and clover, stand up, akihabara@deep... gosh i've seen so many it's hard to remember. I also recommend Pride and Nobuta wo produce.
my mind is flooded with titles so maybe you should say what type of dramas you'd prefer or try some of these and see what you like and dislike.
