Memento Mori is totally addicting, I've seen it several times and it's always a thrill. The acting is great and Kim Min-Sun is so cute! Go for the Korean version even though it's supposed to be region 3 it's actually all-region. I played it on my JVC just fine. I've also watched the overseas region 1 version but the quality isn't as good and I believe it was missing some scenes (I could be wrong about that). The Ring Virus is good and if you have an all region player I'd have to recommend My Sassy Girl. The first two movies are horror flicks, but My Sassy Girl is a romantic comedy which unfortunately I had to watch on VHS. Ugh.
You should definitely get the korean movie Musa hen, it follows the Crouching Tiger, Hidden Dragon formula and it even has Zhang Ziyi in it.
It can be ordered from here http://www.hkflix.com for $27 and it's region 3.
Guns and Talk, a good action comedy about a team of hitmen; Tell Me Something, a great detective thriller; My Wife is a Gangster, comedy action a woman who heads a triad??? finds her long lost sister whose dying wish is to see her married.
Chingu is my favorite korean movie. I think it's the higest grossing korean movie ever (it overthrew JSA). Check it out as I have the region free version.