City Hunter, Time Between Dog ans Wolf (kind of a Korean bourne), Bridal Mask (this one looks like a comic book, a little bit a V for Vendetta atmosphere ), Illjimae

also GTO is a good choice.
Liar Game, perhaps My boss my hero Mr Brain, Kagi no kakkata heya
I agree with a lot of the ones mentioned already, and I am assuming drama's without a lot of romance in my suggestions.. Ghost Sign Special Affairs Team TEN Even though I have been watching drama's for 5 almost 6 years now, my husband has never once sat down and watched with me, but he just finished a drama with me, and he liked it, and is watching another one with me off and on, so don't rule out the ones with romance, the one I just finished is Que Sera Sera the one watching right now is Who Are You?
god's quiz and vampire prosecutor
I second Liar Game, Tokyo Dogs, My Boss My Hero, Mr Brain, Kagi no Kakatta Heya Also Bloody Monday, Keizoku 2 SPEC, White Christmas
bloody monday is cool ^^
I wouldn't suggest city hunter, if he hated boys before flowers. Too much fangirl-lee-min-ho romance. I suggest Iris and athena: goddess of war, though I never watched those with guys. But it's action loaded. And japanese dramas are also good because they don't have so much romance. The best thing you can do is to chose a drama based on his interest and which you have already seen. If you know that he likes thrillers why not wath vampire prosecutor with him or some other crime drama. If you know that he likes marterial arts then go with warrior baek dong soo. Or you try out movies first, there are a lot without so much drama XDD
If he likes RPG's (role playing games) then show him Yuusha Yoshihiko to Maou no Shiro. It's the funniest drama of all time.
J-Drama: GTO, Kekkon Dekinai Otoko, My boss my hero, Sora kara furu ichioku no hoshi K-Drama: All In, Chuno , City Hunter, Comrades, Ghost , Giant, H.I.T, IRIS, Jumong, Kingdom of the Wind, Salaryman, Soul, Story of a Man, Swallow the Sun, The Legend, The Devil, Ten, Time Between Dog And Wolf, Tree With Deep Roots, Warrior Baek Dong Soo , White Christmas, East of Eden, Sign
Japan: Umizaru (there are also 2 or 3 movies) for action; Buzzer Beat (rom but it's adult and has great bball scenes), RESCUE (action/drama) SK: Sign for suspense; Harvest Villa for mystery/light comedy; Special Task Force MSS (its only 4 eps long so the commitment is small) TWN: Black & White (crime drama, good chase scenes
Bloody Monday and Holy Land(japanese version) :D