My idea of romantic is a little sturm-und-drang-ish - forgive the ugly word - so it doesn't have to be "hot" for my heart to wrench, break or swell. I hope you don't mind if I focus on the romantic part of the question rather than the hot.
K-drama: Secret Garden - Joo Won talking with imaginary Gil Ra Im while watching the christmas tree and/or their silent talk about him visiting her dreams
K-movie: I haven't watched many romantic k-movies. Not a fan of rom-coms either, so I pass on this one.
...wait, re-thinking of this one, I'd say Duelist has one of the most sensual scenes ever: the dancing fight. Subtly erotic while showing absolutely nothing sexual.
J-drama: Orange Days - Sae complaining about her love being like an empty right hand and Kai asking her to fill the left one with his
J-movie: Tada Kimi Wo Aishiteru - Makoto watching Shizuru's photographic exposition with Shizuru's letter read in voiceover
T-drama: Autumn Concerto - Mu Cheng thanking Guang Xi for the gift he gave her (their child) without him knowing who she's talking about
T-movie: N/A
C-movie: so many... Hero - the "white" scene (I can't elaborate. It's at the end of the movie and I would spoil it)
:)